Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2005, Volume 308, Issue 1, pp. 290 - 302

The main object of this paper is to give analogous definitions of Apostol type (see [T.M. Apostol, On the Lerch Zeta function, Pacific J. Math. 1 (1951)...

Apostol–Euler polynomials of higher order | Hurwitz–Lerch and Lipschitz–Lerch Zeta functions | Hurwitz (or generalized) Zeta function | Apostol–Bernoulli polynomials | Apostol–Bernoulli polynomials of higher order | Bernoulli polynomials | Apostol–Euler polynomials | Gaussian hypergeometric function | Stirling numbers of the second kind | Lerch's functional equation | Hurwitz-Lerch and Lipschitz-Lerch Zeta functions | Apostol-Bernoulli polynomials of higher order | Apostol-Euler polynomials | Apostol-Euler polynomials of higher order | Apostol-Bernoulli polynomials | MATHEMATICS, APPLIED | stirling numbers of the second kind | Apostol-Bemoulli polynomials | MATHEMATICS | EXPLICIT FORMULA | RATIONAL ARGUMENTS | Apostol-Bemoulli polynomials of higher order

Apostol–Euler polynomials of higher order | Hurwitz–Lerch and Lipschitz–Lerch Zeta functions | Hurwitz (or generalized) Zeta function | Apostol–Bernoulli polynomials | Apostol–Bernoulli polynomials of higher order | Bernoulli polynomials | Apostol–Euler polynomials | Gaussian hypergeometric function | Stirling numbers of the second kind | Lerch's functional equation | Hurwitz-Lerch and Lipschitz-Lerch Zeta functions | Apostol-Bernoulli polynomials of higher order | Apostol-Euler polynomials | Apostol-Euler polynomials of higher order | Apostol-Bernoulli polynomials | MATHEMATICS, APPLIED | stirling numbers of the second kind | Apostol-Bemoulli polynomials | MATHEMATICS | EXPLICIT FORMULA | RATIONAL ARGUMENTS | Apostol-Bemoulli polynomials of higher order

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2006, Volume 51, Issue 3, pp. 631 - 642

Recently, Srivastava and Pintér [1] investigated several interesting properties and relationships involving the classical as well as the generalized (or...

Euler polynomials and numbers | ernoulli polynomials and numbers | Generalized (or higher-order) Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Generalized Apostol-Bernoulli polynomials and numbers, Generalized Apostol-Euler polynomials and numbers, Stirling numbers of the second kind, Generating functions, Srivastava-Pintér addition theorems, Recursion formulas | Generalized (or higher-order) Bernoulli polynomials and numbers | Generalized (or higher-order) Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Generalized Apostol-Bernoulli polynomials and numbers, Generalized Apostol-Euler polynomials and numbers | Bernoulli polynomials and numbers | MATHEMATICS, APPLIED | generalized (or higher-order) Euler polynomials and numbers | stirling numbers of the second kind | generalized Apostol-Bernoulli polynomials and numbers | Srivastava-Pinter addition theorems | generating functions | generalized (or higher-order) Bernoulli polynomials and numbers | generalized Apostol-Euler polynomials and numbers | recursion formulas | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Apostol-Euler polynomials and numbers | Apostol-Bernoulli polynomials and numbers | Mathematical models

Euler polynomials and numbers | ernoulli polynomials and numbers | Generalized (or higher-order) Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Generalized Apostol-Bernoulli polynomials and numbers, Generalized Apostol-Euler polynomials and numbers, Stirling numbers of the second kind, Generating functions, Srivastava-Pintér addition theorems, Recursion formulas | Generalized (or higher-order) Bernoulli polynomials and numbers | Generalized (or higher-order) Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Generalized Apostol-Bernoulli polynomials and numbers, Generalized Apostol-Euler polynomials and numbers | Bernoulli polynomials and numbers | MATHEMATICS, APPLIED | generalized (or higher-order) Euler polynomials and numbers | stirling numbers of the second kind | generalized Apostol-Bernoulli polynomials and numbers | Srivastava-Pinter addition theorems | generating functions | generalized (or higher-order) Bernoulli polynomials and numbers | generalized Apostol-Euler polynomials and numbers | recursion formulas | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Apostol-Euler polynomials and numbers | Apostol-Bernoulli polynomials and numbers | Mathematical models

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2015, Volume 431, Issue 1, pp. 34 - 46

We perform a further investigation for the Apostol–Bernoulli and Apostol–Euler polynomials and numbers. By making use of an elementary idea used by Euler in...

Recurrence formulae | Apostol–Bernoulli polynomials and numbers | Apostol–Euler polynomials and numbers | Convolution formulae | A postol-Bernoulli polynomials and numbers | Apostol-Euler polynomials and numbers | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | IDENTITIES | Apostol-Bernoulli polynomials and numbers | FORMULAS

Recurrence formulae | Apostol–Bernoulli polynomials and numbers | Apostol–Euler polynomials and numbers | Convolution formulae | A postol-Bernoulli polynomials and numbers | Apostol-Euler polynomials and numbers | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | IDENTITIES | Apostol-Bernoulli polynomials and numbers | FORMULAS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2008, Volume 199, Issue 2, pp. 723 - 737

In this paper, we first investigate several further interesting properties of the multiple Hurwitz–Lerch Zeta function Φ n ( z, s, a) which was introduced...

q-Extensions of the Apostol–Bernoulli and the Apostol–Euler polynomials and numbers of higher order | Multiple Gamma functions | Multiple Hurwitz–Lerch Zeta function | Riemann Zeta function | Gamma function | Hurwitz–Lerch Zeta function | Series associated with the Zeta function | Hurwitz Zeta function | Hurwitz-Lerch Zeta function | Multiple Hurwitz-Lerch Zeta function | q-Extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials and numbers of higher order | MATHEMATICS, APPLIED | NUMBERS | q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials and numbers of higher order | Q-ANALOGS | DETERMINANTS | GAMMA-FUNCTIONS | gamma function | SUMS | multiple Hurwitz-Lerch Zeta function | FAMILIES | DIRICHLET SERIES | series associated with the Zeta function | FORMULAS | multiple Gamma functions

q-Extensions of the Apostol–Bernoulli and the Apostol–Euler polynomials and numbers of higher order | Multiple Gamma functions | Multiple Hurwitz–Lerch Zeta function | Riemann Zeta function | Gamma function | Hurwitz–Lerch Zeta function | Series associated with the Zeta function | Hurwitz Zeta function | Hurwitz-Lerch Zeta function | Multiple Hurwitz-Lerch Zeta function | q-Extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials and numbers of higher order | MATHEMATICS, APPLIED | NUMBERS | q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials and numbers of higher order | Q-ANALOGS | DETERMINANTS | GAMMA-FUNCTIONS | gamma function | SUMS | multiple Hurwitz-Lerch Zeta function | FAMILIES | DIRICHLET SERIES | series associated with the Zeta function | FORMULAS | multiple Gamma functions

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2012, Volume 81, Issue 279, pp. 1707 - 1722

These results are transferred to the Apostol-Euler polynomials via a simple relation linking them to the Apostol-Bernoulli polynomials.]]>

Integers | Numbers | Approximation | Algebra | Mathematical discontinuity | Generating function | Mathematical constants | Polynomials | Fourier series | Asymptotic estimates | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | MATHEMATICS, APPLIED | asymptotic estimates | Mathematics - Number Theory

Integers | Numbers | Approximation | Algebra | Mathematical discontinuity | Generating function | Mathematical constants | Polynomials | Fourier series | Asymptotic estimates | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | MATHEMATICS, APPLIED | asymptotic estimates | Mathematics - Number Theory

Journal Article

Mathematics, ISSN 2227-7390, 12/2018, Volume 6, Issue 12, p. 329

In this paper, we present a systematic and unified investigation for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi...

Apostol-Euler polynomials | Convolution identities | Stirling numbers of the first and second kind | Apostol-Genocchi polynomials | Apostol-Bernoulli polynomials | FOURIER EXPANSIONS | IDENTITIES | NUMBERS | EXTENSIONS | SUMS | MATHEMATICS | stirling numbers of the first and second kind | PRODUCTS | UNIFICATION | convolution identities

Apostol-Euler polynomials | Convolution identities | Stirling numbers of the first and second kind | Apostol-Genocchi polynomials | Apostol-Bernoulli polynomials | FOURIER EXPANSIONS | IDENTITIES | NUMBERS | EXTENSIONS | SUMS | MATHEMATICS | stirling numbers of the first and second kind | PRODUCTS | UNIFICATION | convolution identities

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2014, Volume 2014, Issue 1, pp. 1 - 13

In this paper, a further investigation for the Apostol-Bernoulli and Apostol-Euler polynomials and numbers is performed. Some closed formulae of sums of...

Bernoulli polynomials and numbers | Euler polynomials and numbers | Ordinary Differential Equations | Apostol-Euler polynomials and numbers | Functional Analysis | summation formulae | Analysis | Difference and Functional Equations | Mathematics, general | Apostol-Bernoulli polynomials and numbers | Mathematics | Partial Differential Equations | Summation formulae | MATHEMATICS | EXPLICIT FORMULA | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | Polynomials | Euler angles | Differential equations | Functions (mathematics) | Difference equations | Production methods | Mathematical analysis | Transforms | Sums

Bernoulli polynomials and numbers | Euler polynomials and numbers | Ordinary Differential Equations | Apostol-Euler polynomials and numbers | Functional Analysis | summation formulae | Analysis | Difference and Functional Equations | Mathematics, general | Apostol-Bernoulli polynomials and numbers | Mathematics | Partial Differential Equations | Summation formulae | MATHEMATICS | EXPLICIT FORMULA | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | Polynomials | Euler angles | Differential equations | Functions (mathematics) | Difference equations | Production methods | Mathematical analysis | Transforms | Sums

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 10

Recently, Tremblay, Gaboury and Fugère introduced a class of the generalized Bernoulli polynomials (see Tremblay in Appl. Math. Let. 24:1888-1893, 2011). In...

Jacobi polynomials | Bernoulli, Euler and Genocchi polynomials | generating functions | Mathematics | Ordinary Differential Equations | Functional Analysis | Laguerre polynomials | Analysis | generalized Apostol-Euler and Apostol-Bernoulli polynomials | Difference and Functional Equations | Mathematics, general | Hermite polynomials | Stirling numbers of the second kind | Partial Differential Equations | Generating functions | Bernoulli-Euler and Genocchi polynomials | Generalized Apostol-Euler and Apostol-Bernoulli polynomials | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | BERNOULLI POLYNOMIALS | MATHEMATICS | GENOCCHI POLYNOMIALS | MULTIPLICATION FORMULAS | Technology application | Usage | Euler angles | Differential equations | Inequalities (Mathematics) | Mathematical optimization

Jacobi polynomials | Bernoulli, Euler and Genocchi polynomials | generating functions | Mathematics | Ordinary Differential Equations | Functional Analysis | Laguerre polynomials | Analysis | generalized Apostol-Euler and Apostol-Bernoulli polynomials | Difference and Functional Equations | Mathematics, general | Hermite polynomials | Stirling numbers of the second kind | Partial Differential Equations | Generating functions | Bernoulli-Euler and Genocchi polynomials | Generalized Apostol-Euler and Apostol-Bernoulli polynomials | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | BERNOULLI POLYNOMIALS | MATHEMATICS | GENOCCHI POLYNOMIALS | MULTIPLICATION FORMULAS | Technology application | Usage | Euler angles | Differential equations | Inequalities (Mathematics) | Mathematical optimization

Journal Article

Advances in Difference Equations, ISSN 1687-1847, 12/2012, Volume 2012, Issue 1, pp. 1 - 16

In this paper, using generating functions and combinatorial techniques, we extend Agoh and Dilcher’s quadratic recurrence formula for Bernoulli numbers in...

Ordinary Differential Equations | Apostol-Euler polynomials and numbers | Functional Analysis | Analysis | Difference and Functional Equations | recurrence formula | Mathematics, general | Apostol-Bernoulli polynomials and numbers | Mathematics | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | IDENTITIES | NUMBERS | Usage | Polynomials | Euler angles | Quadratic functions | Differential equations | Functions (mathematics) | Difference equations | Mathematical analysis | Number theory | Combinatorial analysis

Ordinary Differential Equations | Apostol-Euler polynomials and numbers | Functional Analysis | Analysis | Difference and Functional Equations | recurrence formula | Mathematics, general | Apostol-Bernoulli polynomials and numbers | Mathematics | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | IDENTITIES | NUMBERS | Usage | Polynomials | Euler angles | Quadratic functions | Differential equations | Functions (mathematics) | Difference equations | Mathematical analysis | Number theory | Combinatorial analysis

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 10/2016, Volume 39, Issue 4, pp. 1307 - 1318

In this paper, a further investigation for the Apostol–Bernoulli and Apostol–Euler polynomials is performed, and a new formula of products of the...

Combinatorial identities | Apostol–Euler polynomials and numbers | Mathematics, general | Apostol–Bernoulli polynomials and numbers | 05A19 | Mathematics | Applications of Mathematics | 11B68 | MATHEMATICS | FOURIER EXPANSIONS | Apostol-Euler polynomials and numbers | EXTENSIONS | IDENTITIES | FAMILIES | GENOCCHI POLYNOMIALS | Apostol-Bernoulli polynomials and numbers | MULTIPLICATION FORMULAS | Polynomials

Combinatorial identities | Apostol–Euler polynomials and numbers | Mathematics, general | Apostol–Bernoulli polynomials and numbers | 05A19 | Mathematics | Applications of Mathematics | 11B68 | MATHEMATICS | FOURIER EXPANSIONS | Apostol-Euler polynomials and numbers | EXTENSIONS | IDENTITIES | FAMILIES | GENOCCHI POLYNOMIALS | Apostol-Bernoulli polynomials and numbers | MULTIPLICATION FORMULAS | Polynomials

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 14

The main purpose of this paper is by using the generating function methods and some combinatorial techniques to establish some new recurrence formulae for the...

Apostol-Bernoulli numbers and polynomials | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | Bernoulli numbers and polynomials | combinatorial identities | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | Linear systems | Usage | Polynomials | Euler angles | Research | Innovations

Apostol-Bernoulli numbers and polynomials | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | Bernoulli numbers and polynomials | combinatorial identities | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | HIGHER-ORDER | Linear systems | Usage | Polynomials | Euler angles | Research | Innovations

Journal Article

Filomat, ISSN 0354-5180, 2014, Volume 28, Issue 2, pp. 329 - 351

Carlitz firstly defined the q-Bernoulli and q-Euler polynomials [Duke Math. J., 15(1948), 987-1000]. Recently, M.Cenkci and M.Can [Adv. Stud. Contemp. Math.,...

Generating function | q-Stirling numbers of the second kind | q-Apostol-Bernoulli and q-Apostol-Euler polynomials (of higher order) | q-extension | q-Bernoulli and q-Euler polynomials (of higher order) | Apostol-Bernoulli and Apostol-Euler polynomials (of higher order) | Bernoulli and Euler polynomials (of higher order) | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | NUMBERS | generating function | MATHEMATICS | EXPLICIT FORMULA | ORDER | GENOCCHI POLYNOMIALS

Generating function | q-Stirling numbers of the second kind | q-Apostol-Bernoulli and q-Apostol-Euler polynomials (of higher order) | q-extension | q-Bernoulli and q-Euler polynomials (of higher order) | Apostol-Bernoulli and Apostol-Euler polynomials (of higher order) | Bernoulli and Euler polynomials (of higher order) | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | NUMBERS | generating function | MATHEMATICS | EXPLICIT FORMULA | ORDER | GENOCCHI POLYNOMIALS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 9, pp. 3591 - 3602

A unification (and generalization) of various Apostol type polynomials was introduced and investigated recently by Luo and Srivastava [Q.-M. Luo,...

Generalized Apostol type polynomials | Generalized sum of integer powers | Generalized Apostol–Bernoulli polynomials | Genocchi polynomials of higher order | Generalized Apostol–Euler polynomials | Generalized alternating sum | Generalized ApostolBernoulli polynomials | Generalized ApostolEuler polynomials | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | BERNOULLI | Generalized Apostol-Euler polynomials | Generalized Apostol-Bernoulli polynomials | ORDER | EULER POLYNOMIALS | GENOCCHI POLYNOMIALS | FORMULAS | Integers | Mathematical models | Mathematical analysis | Symmetry

Generalized Apostol type polynomials | Generalized sum of integer powers | Generalized Apostol–Bernoulli polynomials | Genocchi polynomials of higher order | Generalized Apostol–Euler polynomials | Generalized alternating sum | Generalized ApostolBernoulli polynomials | Generalized ApostolEuler polynomials | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | BERNOULLI | Generalized Apostol-Euler polynomials | Generalized Apostol-Bernoulli polynomials | ORDER | EULER POLYNOMIALS | GENOCCHI POLYNOMIALS | FORMULAS | Integers | Mathematical models | Mathematical analysis | Symmetry

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 8/2019, Volume 49, Issue 3, pp. 567 - 583

We show that any Appell sequence can be written in closed form as a forward difference transformation of the identity. Such transformations are actually...

33C45 | Functions of a Complex Variable | Forward difference transformation | Appell polynomials | Field Theory and Polynomials | Higher order convolution identities | Mathematics | 11B68 | Generalized Bernoulli polynomials | Fourier Analysis | Binomial convolution | Number Theory | Generalized Apostol–Euler polynomials | Combinatorics | 60E05 | IDENTITIES | Generalized Apostol-Euler polynomials | CONVOLUTION | SUMS | MATHEMATICS | EXPLICIT FORMULA | HIGHER-ORDER | PRODUCTS | APOSTOL-BERNOULLI | EULER

33C45 | Functions of a Complex Variable | Forward difference transformation | Appell polynomials | Field Theory and Polynomials | Higher order convolution identities | Mathematics | 11B68 | Generalized Bernoulli polynomials | Fourier Analysis | Binomial convolution | Number Theory | Generalized Apostol–Euler polynomials | Combinatorics | 60E05 | IDENTITIES | Generalized Apostol-Euler polynomials | CONVOLUTION | SUMS | MATHEMATICS | EXPLICIT FORMULA | HIGHER-ORDER | PRODUCTS | APOSTOL-BERNOULLI | EULER

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2011, Volume 24, Issue 11, pp. 1888 - 1893

The main purpose of this paper is to introduce and investigate a new class of generalized Apostol–Bernoulli polynomials based on a definition given by Natalini...

Generalized Euler polynomials | Generalized Apostol–Bernoulli polynomials | Generalized Apostol–Euler polynomials | Stirling numbers of the second kind | Generating functions | Generalized Bernoulli polynomials | Generalized Apostol-Bernoulli polynomials | Generalized ApostolEuler polynomials | MATHEMATICS, APPLIED | HIGHER-ORDER | EULER POLYNOMIALS | HURWITZ ZETA-FUNCTION | Generalized Apostol-Euler polynomials | FORMULAS | Heterocyclic compounds | Analogue | Lists | Mathematical analysis | Addition theorem

Generalized Euler polynomials | Generalized Apostol–Bernoulli polynomials | Generalized Apostol–Euler polynomials | Stirling numbers of the second kind | Generating functions | Generalized Bernoulli polynomials | Generalized Apostol-Bernoulli polynomials | Generalized ApostolEuler polynomials | MATHEMATICS, APPLIED | HIGHER-ORDER | EULER POLYNOMIALS | HURWITZ ZETA-FUNCTION | Generalized Apostol-Euler polynomials | FORMULAS | Heterocyclic compounds | Analogue | Lists | Mathematical analysis | Addition theorem

Journal Article

Results in Mathematics, ISSN 1422-6383, 9/2015, Volume 68, Issue 1, pp. 203 - 225

Under a slight modification on the parameters associated to the generalized Apostol-type polynomials and the use of the generating method, we obtain some new...

11C08 | Generalized Apostol-type polynomials | 33B99 | Apostol–Euler polynomials of higher order | 11M35 | 05A10 | Apostol–Genocchi polynomials of higher order | 11B65 | stirling numbers of second kind | Mathematics, general | Apostol–Bernoulli polynomials of higher order | Mathematics | MATHEMATICS | EXPLICIT FORMULA | MATHEMATICS, APPLIED | HIGHER-ORDER | Apostol-Bernoulli polynomials of higher order | BERNOULLI POLYNOMIALS | Apostol-Euler polynomials of higher order | Apostol-Genocchi polynomials of higher order | EULER

11C08 | Generalized Apostol-type polynomials | 33B99 | Apostol–Euler polynomials of higher order | 11M35 | 05A10 | Apostol–Genocchi polynomials of higher order | 11B65 | stirling numbers of second kind | Mathematics, general | Apostol–Bernoulli polynomials of higher order | Mathematics | MATHEMATICS | EXPLICIT FORMULA | MATHEMATICS, APPLIED | HIGHER-ORDER | Apostol-Bernoulli polynomials of higher order | BERNOULLI POLYNOMIALS | Apostol-Euler polynomials of higher order | Apostol-Genocchi polynomials of higher order | EULER

Journal Article

Mathematical and Computer Modelling, ISSN 0895-7177, 2010, Volume 52, Issue 1, pp. 247 - 259

By using certain operational methods, the authors introduce a family of Laguerre-based Appell polynomials. Some properties of Laguerre–Appell polynomials are...

Monomiality principle | Apostol–Euler polynomials | 2-variable Laguerre polynomials | Laguerre–Appell polynomials | Apostol–Bernoulli polynomials | Laguerre-Appell polynomials | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | GENERALIZED POLYNOMIALS | MATHEMATICS, APPLIED | EULER POLYNOMIALS | MONOMIALITY | BERNOULLI

Monomiality principle | Apostol–Euler polynomials | 2-variable Laguerre polynomials | Laguerre–Appell polynomials | Apostol–Bernoulli polynomials | Laguerre-Appell polynomials | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | GENERALIZED POLYNOMIALS | MATHEMATICS, APPLIED | EULER POLYNOMIALS | MONOMIALITY | BERNOULLI

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 3, pp. 906 - 911

Recently, Srivastava et al. introduced a new generalization of the Bernoulli, Euler and Genocchi polynomials (see [H.M. Srivastava, M. Garg, S. Choudhary,...

Generating function | Euler polynomials | Apostol–Bernoulli polynomials | Apostol–Bernoulli polynomials of order α | Bernoulli numbers and polynomials | Hurwitz-Lerch zeta functions | Apostol–Euler polynomials | Consecutive sums | Apostol-Bernoulli polynomials of order α | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | MATHEMATICS, APPLIED | NUMBERS | ZETA | Apostol-Bernoulli polynomials of order alpha | APOSTOL-BERNOULLI | FORMULAS | Hypergeometric functions | Interpolation | Multiplication | Computation | Mathematical analysis | Gaussian | Mathematical models | Sums

Generating function | Euler polynomials | Apostol–Bernoulli polynomials | Apostol–Bernoulli polynomials of order α | Bernoulli numbers and polynomials | Hurwitz-Lerch zeta functions | Apostol–Euler polynomials | Consecutive sums | Apostol-Bernoulli polynomials of order α | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | MATHEMATICS, APPLIED | NUMBERS | ZETA | Apostol-Bernoulli polynomials of order alpha | APOSTOL-BERNOULLI | FORMULAS | Hypergeometric functions | Interpolation | Multiplication | Computation | Mathematical analysis | Gaussian | Mathematical models | Sums

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 06/2017, Volume 14, Issue 3, p. 1

The aim of this paper is to give generating functions and to prove various properties for some new families of special polynomials and numbers. Several...

Bernoulli polynomials and numbers | Euler polynomials and numbers | Humbert polynomials | Genocchi polynomials | Generating function | Apostol–Euler polynomials and numbers | Apostol–Bernoulli polynomials and numbers | Fibonacci polynomials | Stirling numbers | MATHEMATICS, APPLIED | UNIFIED PRESENTATION | BERNOULLI | MATHEMATICS | Apostol-Euler polynomials and numbers | FAMILIES | Apostol-Bernoulli polynomials and numbers | EULER

Bernoulli polynomials and numbers | Euler polynomials and numbers | Humbert polynomials | Genocchi polynomials | Generating function | Apostol–Euler polynomials and numbers | Apostol–Bernoulli polynomials and numbers | Fibonacci polynomials | Stirling numbers | MATHEMATICS, APPLIED | UNIFIED PRESENTATION | BERNOULLI | MATHEMATICS | Apostol-Euler polynomials and numbers | FAMILIES | Apostol-Bernoulli polynomials and numbers | EULER

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2018, Volume 41, Issue 16, pp. 6934 - 6954

The aim of this paper is to construct a new method related to a family of operators to define generating functions for special numbers and polynomials. With...

Bernoulli polynomials and numbers | differential equation | functional equations | Apostol‐Bernoulli polynomials and numbers | central factorial numbers | generating function | Apostol‐Euler polynomials and numbers | Lagrange inversion formula operators | Fourier series | Stirling numbers | combinatorial sum | Apostol-Euler polynomials and numbers | Apostol-Bernoulli polynomials and numbers | MATHEMATICS, APPLIED | IDENTITIES | COMBINATORIAL SUMS | BERNOULLI | ZETA | EULER | Hyperbolic functions | Markov analysis | Power series | Sums | Operators (mathematics) | Numbers | Convolution | Functional equations | Mathematical analysis | Integrals | Construction methods | Differential equations | Polynomials | Trigonometric functions | Formulas (mathematics) | Combinatorial analysis

Bernoulli polynomials and numbers | differential equation | functional equations | Apostol‐Bernoulli polynomials and numbers | central factorial numbers | generating function | Apostol‐Euler polynomials and numbers | Lagrange inversion formula operators | Fourier series | Stirling numbers | combinatorial sum | Apostol-Euler polynomials and numbers | Apostol-Bernoulli polynomials and numbers | MATHEMATICS, APPLIED | IDENTITIES | COMBINATORIAL SUMS | BERNOULLI | ZETA | EULER | Hyperbolic functions | Markov analysis | Power series | Sums | Operators (mathematics) | Numbers | Convolution | Functional equations | Mathematical analysis | Integrals | Construction methods | Differential equations | Polynomials | Trigonometric functions | Formulas (mathematics) | Combinatorial analysis

Journal Article

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