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

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 2013, Volume 36, Issue 2, pp. 465 - 479

The present paper deals with multiplication formulas for the Apostol-Genocchi polynomials of higher order and deduces some explicit recursive formulas. Some...

Raabe's multiplication formula | Euler numbers and polynomials | Bernoulli numbers and polynomials | Multiplication formula | Stirling numbers | Apostol-Genocchi numbers and polynomials (of higher order) | Generalization of Genocchi numbers and polynomials | BERNOULLI NUMBERS | generalization of Genocchi numbers and polynomials | MATHEMATICS | multiplication formula | ZETA | EULER POLYNOMIALS | EXPLICIT FORMULAS | Q-EXTENSION

Raabe's multiplication formula | Euler numbers and polynomials | Bernoulli numbers and polynomials | Multiplication formula | Stirling numbers | Apostol-Genocchi numbers and polynomials (of higher order) | Generalization of Genocchi numbers and polynomials | BERNOULLI NUMBERS | generalization of Genocchi numbers and polynomials | MATHEMATICS | multiplication formula | ZETA | EULER POLYNOMIALS | EXPLICIT FORMULAS | Q-EXTENSION

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2011, Volume 217, Issue 12, pp. 5702 - 5728

Recently, the authors introduced some generalizations of the Apostol–Bernoulli polynomials and the Apostol–Euler polynomials (see [Q.-M. Luo, H.M. Srivastava,...

Lerch’s functional equation | Hurwitz (or generalized), Hurwitz–Lerch and Lipschitz–Lerch zeta functions | Srivastava’s formula and Gaussian hypergeometric function | Genocchi numbers and Genocchi polynomials of higher order | Stirling numbers and the λ-Stirling numbers of the second kind | Apostol–Genocchi numbers and Apostol–Genocchi polynomials of higher order | Apostol–Bernoulli polynomials and Apostol–Euler polynomials of higher order | Apostol–Genocchi numbers and Apostol–Genocchi polynomials | Apostol-Bernoulli polynomials and Apostol-Euler polynomials of higher order | Srivastava's formula and Gaussian hypergeometric function | Hurwitz (or generalized), Hurwitz-Lerch and Lipschitz-Lerch zeta functions | Apostol-Genocchi numbers and Apostol-Genocchi polynomials | Apostol-Genocchi numbers and Apostol-Genocchi polynomials of higher order | Lerch's functional equation | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | IDENTITIES | Q-EXTENSIONS | BERNOULLI | EXPLICIT FORMULA | ORDER | Stirling numbers and the lambda-Stirling numbers of the second kind | EULER POLYNOMIALS | INTEGRAL-REPRESENTATIONS | Hypergeometric functions | Analogue | Computation | Mathematical analysis | Gaussian | Mathematical models | Error correction | Representations

Lerch’s functional equation | Hurwitz (or generalized), Hurwitz–Lerch and Lipschitz–Lerch zeta functions | Srivastava’s formula and Gaussian hypergeometric function | Genocchi numbers and Genocchi polynomials of higher order | Stirling numbers and the λ-Stirling numbers of the second kind | Apostol–Genocchi numbers and Apostol–Genocchi polynomials of higher order | Apostol–Bernoulli polynomials and Apostol–Euler polynomials of higher order | Apostol–Genocchi numbers and Apostol–Genocchi polynomials | Apostol-Bernoulli polynomials and Apostol-Euler polynomials of higher order | Srivastava's formula and Gaussian hypergeometric function | Hurwitz (or generalized), Hurwitz-Lerch and Lipschitz-Lerch zeta functions | Apostol-Genocchi numbers and Apostol-Genocchi polynomials | Apostol-Genocchi numbers and Apostol-Genocchi polynomials of higher order | Lerch's functional equation | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | IDENTITIES | Q-EXTENSIONS | BERNOULLI | EXPLICIT FORMULA | ORDER | Stirling numbers and the lambda-Stirling numbers of the second kind | EULER POLYNOMIALS | INTEGRAL-REPRESENTATIONS | Hypergeometric functions | Analogue | Computation | Mathematical analysis | Gaussian | Mathematical models | Error correction | Representations

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

Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 13

In this paper, we introduce a unified family of Hermite-based Apostol-Bernoulli, Euler and Genocchi polynomials. We obtain some symmetry identities between...

generalized sum of alternative integer powers | Ordinary Differential Equations | Functional Analysis | Hermite-based Apostol-Genocchi polynomials | Analysis | Difference and Functional Equations | generalized sum of integer powers | Mathematics, general | Hermite-based Apostol-Euler polynomials | Mathematics | Partial Differential Equations | Hermite-based Apostol-Bernoulli polynomials | Generalized sum of alternative integer powers | Generalized sum of integer powers | MATHEMATICS, APPLIED | EXTENSIONS | NUMBERS | GENERATING-FUNCTIONS | SUM | MATHEMATICS | SYMMETRY | FORMULAS | Usage | Euler angles | Gaussian processes

generalized sum of alternative integer powers | Ordinary Differential Equations | Functional Analysis | Hermite-based Apostol-Genocchi polynomials | Analysis | Difference and Functional Equations | generalized sum of integer powers | Mathematics, general | Hermite-based Apostol-Euler polynomials | Mathematics | Partial Differential Equations | Hermite-based Apostol-Bernoulli polynomials | Generalized sum of alternative integer powers | Generalized sum of integer powers | MATHEMATICS, APPLIED | EXTENSIONS | NUMBERS | GENERATING-FUNCTIONS | SUM | MATHEMATICS | SYMMETRY | FORMULAS | Usage | Euler angles | Gaussian processes

Journal Article

SpringerPlus, ISSN 2193-1801, 12/2016, Volume 5, Issue 1, pp. 1 - 17

By using the modified Milne-Thomson’s polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803–2808, 2014), we introduce a new concept of the Apostol...

Summation formulae | Genocchi polynomials | Hermite–Genocchi polynomials | Apostol-Genocchi polynomials | Symmetric identities | 05A10 | Science | Hermite polynomials | 11B68 | 05A15 | Science, general | GAUSS HYPERGEOMETRIC-FUNCTIONS | UMBRAL CALCULUS | NUMBERS | EXTENSIONS | MULTIDISCIPLINARY SCIENCES | BERNOULLI POLYNOMIALS | HIGHER-ORDER | Hermite-Genocchi polynomials | EULER POLYNOMIALS | IMPLICIT SUMMATION FORMULAS

Summation formulae | Genocchi polynomials | Hermite–Genocchi polynomials | Apostol-Genocchi polynomials | Symmetric identities | 05A10 | Science | Hermite polynomials | 11B68 | 05A15 | Science, general | GAUSS HYPERGEOMETRIC-FUNCTIONS | UMBRAL CALCULUS | NUMBERS | EXTENSIONS | MULTIDISCIPLINARY SCIENCES | BERNOULLI POLYNOMIALS | HIGHER-ORDER | Hermite-Genocchi polynomials | EULER POLYNOMIALS | IMPLICIT SUMMATION FORMULAS

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2016, Volume 2016, Issue 1, pp. 1 - 18

In the year 2014, Kim et al. computed a kind of new sums of the products of an arbitrary number of the classical Bernoulli and Euler polynomials by using the...

Mathematics | Apostol-Euler polynomials | 11B68 | Apostol-Bernoulli polynomials | summation formulas | recurrence relations | Ordinary Differential Equations | Functional Analysis | Analysis | Apostol-Genocchi polynomials | Difference and Functional Equations | Mathematics, general | 05A19 | Partial Differential Equations | FOURIER EXPANSIONS | COMPLETE SUM | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | EXTENSIONS | BERNOULLI | MATHEMATICS | EULER POLYNOMIALS | Difference equations | Mathematical analysis | Transforms | Polynomials | Vector spaces | Formulas (mathematics) | Sums

Mathematics | Apostol-Euler polynomials | 11B68 | Apostol-Bernoulli polynomials | summation formulas | recurrence relations | Ordinary Differential Equations | Functional Analysis | Analysis | Apostol-Genocchi polynomials | Difference and Functional Equations | Mathematics, general | 05A19 | Partial Differential Equations | FOURIER EXPANSIONS | COMPLETE SUM | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | EXTENSIONS | BERNOULLI | MATHEMATICS | EULER POLYNOMIALS | Difference equations | Mathematical analysis | Transforms | Polynomials | Vector spaces | Formulas (mathematics) | Sums

Journal Article

Utilitas Mathematica, ISSN 0315-3681, 11/2012, Volume 89, pp. 179 - 191

We obtain the multiplication formulas for the Apostol-Genocchi polynomials of higher order by using the generalized multinomial identity. We introduce the...

MATHEMATICS, APPLIED | lambda-multiple alternating sums | NUMBERS | IDENTITIES | Apostol-Genocchi numbers and polynomials of higher order | BERNOULLI POLYNOMIALS | STATISTICS & PROBABILITY | multinomial identity | multiplication formula | HIGHER-ORDER | EULER POLYNOMIALS | Apostol-Bernoulli numbers and polynomials of higher order | RECURRENCE

MATHEMATICS, APPLIED | lambda-multiple alternating sums | NUMBERS | IDENTITIES | Apostol-Genocchi numbers and polynomials of higher order | BERNOULLI POLYNOMIALS | STATISTICS & PROBABILITY | multinomial identity | multiplication formula | HIGHER-ORDER | EULER POLYNOMIALS | Apostol-Bernoulli numbers and polynomials of higher order | RECURRENCE

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2019, Volume 113, Issue 4, pp. 3253 - 3267

By introducing two specific generating functions, we define a kind of parametric Fubini-type polynomials. We investigate some fundamental properties of these...

Secondary 12D10 | Theoretical, Mathematical and Computational Physics | Appell polynomials | Generating functions | Mathematics | Apostol–Genocchi polynomials | Primary 11B68 | 30C15 | Fubini type polynomials | 11B83 | Apostol–Bernoulli polynomials | 11B73 | Mathematics, general | 05A19 | Applications of Mathematics | Apostol–Euler polynomials | 05A15 | 26C05 | Multilinear and multilateral generating functions | IDENTITIES | NUMBERS | UNIFIED PRESENTATION | BERNOULLI | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | GENERALIZED APOSTOL TYPE | MATHEMATICS | Apostol-Genocchi polynomials | EULER POLYNOMIALS | FAMILIES | Functions (mathematics) | Mathematical analysis | Polynomials

Secondary 12D10 | Theoretical, Mathematical and Computational Physics | Appell polynomials | Generating functions | Mathematics | Apostol–Genocchi polynomials | Primary 11B68 | 30C15 | Fubini type polynomials | 11B83 | Apostol–Bernoulli polynomials | 11B73 | Mathematics, general | 05A19 | Applications of Mathematics | Apostol–Euler polynomials | 05A15 | 26C05 | Multilinear and multilateral generating functions | IDENTITIES | NUMBERS | UNIFIED PRESENTATION | BERNOULLI | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | GENERALIZED APOSTOL TYPE | MATHEMATICS | Apostol-Genocchi polynomials | EULER POLYNOMIALS | FAMILIES | Functions (mathematics) | Mathematical analysis | Polynomials

Journal Article

Journal of Nonlinear Science and Applications, ISSN 2008-1898, 2016, Volume 9, Issue 6, pp. 4780 - 4797

We perform a further investigation for the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. By making use of the generating function methods...

Apostol-Bernoulli polynomials and numbers | Apostol-Euler polynomials and numbers | Combinatorial identities | Apostol-Genocchi polynomials and numbers | MATHEMATICS | FOURIER EXPANSIONS | HIGHER-ORDER | RECURRENCES | PRODUCTS | combinatorial identities | FORMULAS

Apostol-Bernoulli polynomials and numbers | Apostol-Euler polynomials and numbers | Combinatorial identities | Apostol-Genocchi polynomials and numbers | MATHEMATICS | FOURIER EXPANSIONS | HIGHER-ORDER | RECURRENCES | PRODUCTS | combinatorial identities | FORMULAS

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 10/2014, Volume 37, Issue 15, pp. 2198 - 2210

Recently, Srivastava and Pintér proved addition theorems for the generalized Bernoulli and Euler polynomials. Luo and Srivastava obtained the anologous results...

2D‐Appell Polynomials | Apostol–Euler polynomials | Apostol–Genocchi polynomials | Appell Polynomials | Stirling numbers of the second type | Apostol–Bernoulli polynomials | 2D-Appell polynomials | Apostol-Euler polynomials | Apostol-Genocchi polynomials | Appell polynomials | Apostol-Bernoulli polynomials | 2D-Appell Polynomials | MATHEMATICS, APPLIED | EULER | Functions (mathematics) | Hypergeometric functions | Theorems | Mathematical analysis | Addition theorem | Polynomials | Representations | Combinatorial analysis

2D‐Appell Polynomials | Apostol–Euler polynomials | Apostol–Genocchi polynomials | Appell Polynomials | Stirling numbers of the second type | Apostol–Bernoulli polynomials | 2D-Appell polynomials | Apostol-Euler polynomials | Apostol-Genocchi polynomials | Appell polynomials | Apostol-Bernoulli polynomials | 2D-Appell Polynomials | MATHEMATICS, APPLIED | EULER | Functions (mathematics) | Hypergeometric functions | Theorems | Mathematical analysis | Addition theorem | Polynomials | Representations | Combinatorial analysis

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 2/2011, Volume 15, Issue 1, pp. 283 - 305

The main object of this paper is to introduce and investigate a new generalization of the family of Euler polynomials by means of a suitable generating...

Hypergeometric functions | Series convergence | Polynomials | Generating function | Coefficients | New family | Gauss summation theorem | Genocchi polynomials | Taylor-Maclaurin series expansion | NUMBERS | IDENTITIES | Euler polynomials | Hurwitz-Lerch Zeta function | Pfaff-Kummer transformation | LERCH ZETA-FUNCTIONS | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | Leibniz rule | MATHEMATICS | HIGHER-ORDER | Apostol-Genocchi polynomials | Bernoulli polynomials | INTEGRAL-REPRESENTATIONS | Gaussian hypergeometric function | Stirling numbers of the second kind | RATIONAL ARGUMENTS | FORMULAS

Hypergeometric functions | Series convergence | Polynomials | Generating function | Coefficients | New family | Gauss summation theorem | Genocchi polynomials | Taylor-Maclaurin series expansion | NUMBERS | IDENTITIES | Euler polynomials | Hurwitz-Lerch Zeta function | Pfaff-Kummer transformation | LERCH ZETA-FUNCTIONS | Apostol-Euler polynomials | Apostol-Bernoulli polynomials | Leibniz rule | MATHEMATICS | HIGHER-ORDER | Apostol-Genocchi polynomials | Bernoulli polynomials | INTEGRAL-REPRESENTATIONS | Gaussian hypergeometric function | Stirling numbers of the second kind | RATIONAL ARGUMENTS | FORMULAS

Journal Article

Mathematical Notes, ISSN 0001-4346, 2/2012, Volume 91, Issue 1, pp. 46 - 57

We investigate multiplication formulas for Apostol-type polynomials and introduce λ-multiple alternating sums, which are evaluated by Apostol-type polynomials....

Apostol-Bernoulli numbers and polynomials | recursive formula | λ-multiple alternating sum | Apostol-type polynomials | Raabe’s multiplication formula | alternating sum | Apostol-Euler numbers and polynomials | Mathematics, general | Mathematics | generalized multinomial identity | Apostol-Genocchi numbers and polynomials | multinomial identity | Raabe's multiplication formula | MATHEMATICS | BERNOULLI | lambda-multiple alternating sum

Apostol-Bernoulli numbers and polynomials | recursive formula | λ-multiple alternating sum | Apostol-type polynomials | Raabe’s multiplication formula | alternating sum | Apostol-Euler numbers and polynomials | Mathematics, general | Mathematics | generalized multinomial identity | Apostol-Genocchi numbers and polynomials | multinomial identity | Raabe's multiplication formula | MATHEMATICS | BERNOULLI | lambda-multiple alternating sum

Journal Article

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