2007, MAA tercentenary Euler celebration, ISBN 0883855658, Volume 5, xvi, 298

Book

SpringerPlus, ISSN 2193-1801, 12/2013, Volume 2, Issue 1, pp. 1 - 14

Motivated essentially by recent works by several authors (see, for example, Bin-Saad [Math J Okayama Univ 49:37–52, 2007] and Katsurada [Publ Inst Math...

General Hurwitz-Lerch Zeta function | Lerch Zeta function and the Polylogarithmic (or de Jonquière’s) function | Hurwitz (or generalized) and Hurwitz-Lerch Zeta functions | Generating functions and Eulerian Gamma-function and Beta-function integral representations | Fox-Wright Ψ -function and the -function | Mittag-Leffler type functions | Gauss and Kummer hypergeometric functions | Mellin-Barnes type integral representations and Meromorphic continuation | Riemann | Science, general | Fox-Wright 9-function and the H-function | Lerch Zeta function and the Polylogarithmic (or de Jonquière's) function | Lerch Zeta function and the Polylogarithmic (or de Jonquiere's) function | SERIES | MULTIDISCIPLINARY SCIENCES | BERNOULLI | POLYNOMIALS | Fox-Wright Psi-function and the (H)over-bar-function | FEYNMAN-INTEGRALS | FORMULAS | EULER

General Hurwitz-Lerch Zeta function | Lerch Zeta function and the Polylogarithmic (or de Jonquière’s) function | Hurwitz (or generalized) and Hurwitz-Lerch Zeta functions | Generating functions and Eulerian Gamma-function and Beta-function integral representations | Fox-Wright Ψ -function and the -function | Mittag-Leffler type functions | Gauss and Kummer hypergeometric functions | Mellin-Barnes type integral representations and Meromorphic continuation | Riemann | Science, general | Fox-Wright 9-function and the H-function | Lerch Zeta function and the Polylogarithmic (or de Jonquière's) function | Lerch Zeta function and the Polylogarithmic (or de Jonquiere's) function | SERIES | MULTIDISCIPLINARY SCIENCES | BERNOULLI | POLYNOMIALS | Fox-Wright Psi-function and the (H)over-bar-function | FEYNMAN-INTEGRALS | FORMULAS | EULER

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 2/2019, Volume 291, Issue 1, pp. 711 - 739

We prove that all Langlands–Shahidi automorphic L-functions over function fields are rational; after twists by highly ramified characters they become...

22E50 | Mathematics, general | Mathematics | Primary 11F70 | 22E55 | MATHEMATICS | REDUCTIVE GROUPS | CLASSIFICATION | EISENSTEIN SERIES | EULER PRODUCTS

22E50 | Mathematics, general | Mathematics | Primary 11F70 | 22E55 | MATHEMATICS | REDUCTIVE GROUPS | CLASSIFICATION | EISENSTEIN SERIES | EULER PRODUCTS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 10, pp. 2779 - 2787

The goal of this paper is to unify and extend the generating functions of the generalized Bernoulli polynomials, the generalized Euler polynomials and the...

Riemann and Hurwitz (or generalized) zeta functions | Polylogarithm function | Lipschitz–Lerch zeta function | Euler numbers and Euler polynomials | Lerch zeta function | Bernoulli numbers and Bernoulli polynomials | Genocchi numbers and Genocchi polynomials | Recurrence relations | Hurwitz–Lerch zeta function | Mellin transformation | Dirichlet character | LipschitzLerch zeta function | HurwitzLerch zeta function | MATHEMATICS, APPLIED | Hurwitz-Lerch zeta function | NUMBERS | EXTENSION | Lipschitz-Lerch zeta function | ZETA | APOSTOL-BERNOULLI | FORMULAS | Genocchi numbers and Genocch polynomials | Construction | Mathematical models | Transformations | Mathematical analysis

Riemann and Hurwitz (or generalized) zeta functions | Polylogarithm function | Lipschitz–Lerch zeta function | Euler numbers and Euler polynomials | Lerch zeta function | Bernoulli numbers and Bernoulli polynomials | Genocchi numbers and Genocchi polynomials | Recurrence relations | Hurwitz–Lerch zeta function | Mellin transformation | Dirichlet character | LipschitzLerch zeta function | HurwitzLerch zeta function | MATHEMATICS, APPLIED | Hurwitz-Lerch zeta function | NUMBERS | EXTENSION | Lipschitz-Lerch zeta function | ZETA | APOSTOL-BERNOULLI | FORMULAS | Genocchi numbers and Genocch polynomials | Construction | Mathematical models | Transformations | Mathematical analysis

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 844 - 858

In the paper, by induction, the Faà di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher...

Bell polynomial of the second kind | Tangent number | Bernoulli number | Explicit formula | Derivative polynomial | Euler polynomial | MATHEMATICS, APPLIED | BERNOULLI NUMBERS | INEQUALITIES | IDENTITIES | COMPLETE MONOTONICITY | STIRLING NUMBERS | POLYNOMIALS | EXPLICIT FORMULAS | INTEGRAL-REPRESENTATION | 2ND KIND | 1ST KIND

Bell polynomial of the second kind | Tangent number | Bernoulli number | Explicit formula | Derivative polynomial | Euler polynomial | MATHEMATICS, APPLIED | BERNOULLI NUMBERS | INEQUALITIES | IDENTITIES | COMPLETE MONOTONICITY | STIRLING NUMBERS | POLYNOMIALS | EXPLICIT FORMULAS | INTEGRAL-REPRESENTATION | 2ND KIND | 1ST KIND

Journal Article

1996, ISBN 9780471113133, xii, 374

This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value...

Functions, Special | Boundary value problems | Mathematical physics

Functions, Special | Boundary value problems | Mathematical physics

Book

Russian Journal of Mathematical Physics, ISSN 1061-9208, 04/2017, Volume 24, Issue 2, pp. 241 - 248

In this paper, we introduce the degenerate Laplace transform and degenerate gamma function and investigate some of their properties. From our investigation, we...

POLYNOMIALS | IDENTITIES | PHYSICS, MATHEMATICAL | EULER NUMBERS | Mathematics - Number Theory

POLYNOMIALS | IDENTITIES | PHYSICS, MATHEMATICAL | EULER NUMBERS | Mathematics - Number Theory

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2006, Volume 19, Issue 10, pp. 1073 - 1077

The authors derive a linear ODE (ordinary differential equation) whose particular solution is the Butzer–Flocke–Hauss complete real-parameter Omega function Ω...

Bessel function | Butzer–Flocke–Hauss complete Omega function | Complex-index Euler function | Alternating Mathieu series | Complex-index Bernoulli function | Riemann’s Zeta function | Integral representations of alternating Mathieu series | Integral representation of the Omega function | Dirichlet’s Eta function | Butzer-Flocke-Hauss complete Omega function | Dirichlet's Eta function | Riemann's Zeta function | MATHEMATICS, APPLIED | integral representation of the Omega factor | complete-index Euler function | integral representations of alternating Mathieu series | alternating Mathieu series

Bessel function | Butzer–Flocke–Hauss complete Omega function | Complex-index Euler function | Alternating Mathieu series | Complex-index Bernoulli function | Riemann’s Zeta function | Integral representations of alternating Mathieu series | Integral representation of the Omega function | Dirichlet’s Eta function | Butzer-Flocke-Hauss complete Omega function | Dirichlet's Eta function | Riemann's Zeta function | MATHEMATICS, APPLIED | integral representation of the Omega factor | complete-index Euler function | integral representations of alternating Mathieu series | alternating Mathieu series

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2014, Volume 247, pp. 348 - 352

Formulas and identities involving many well-known special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) play...

Gauss hypergeometric function | Generalized Beta functions | Generalized Gauss type hypergeometric functions | Gamma and Beta functions | Generating functions | Beta functions | Gamma and | Gauss type hypergeometric functions | Generalized | MATHEMATICS, APPLIED | SYMBOL | EXTENSION | EULER | FAMILY | BETA | Hypergeometric functions | Mathematical models | Computation | Mathematical analysis

Gauss hypergeometric function | Generalized Beta functions | Generalized Gauss type hypergeometric functions | Gamma and Beta functions | Generating functions | Beta functions | Gamma and | Gauss type hypergeometric functions | Generalized | MATHEMATICS, APPLIED | SYMBOL | EXTENSION | EULER | FAMILY | BETA | Hypergeometric functions | Mathematical models | Computation | Mathematical analysis

Journal Article

Review of Scientific Instruments, ISSN 0034-6748, 10/2018, Volume 89, Issue 10, p. 105001

The measurement of hand kinematics is important for the assessment and rehabilitation of the paralysed hand. The traditional method of hand function assessment...

SYSTEMS | INSTRUMENTS & INSTRUMENTATION | PHYSICS, APPLIED | THERAPY | MOTION | Euler angles | Inertial sensing devices | Calibration | Rotation | Yaw | Rangefinding | Motion sensors | Rolling motion | Wrist | Goniometers | Elbow (anatomy) | Kinematics | Pitch (inclination) | Sensors | Rehabilitation

SYSTEMS | INSTRUMENTS & INSTRUMENTATION | PHYSICS, APPLIED | THERAPY | MOTION | Euler angles | Inertial sensing devices | Calibration | Rotation | Yaw | Rangefinding | Motion sensors | Rolling motion | Wrist | Goniometers | Elbow (anatomy) | Kinematics | Pitch (inclination) | Sensors | Rehabilitation

Journal Article

Systems & Control Letters, ISSN 0167-6911, 06/2017, Volume 104, pp. 66 - 71

A new explicit Lyapunov function allows to study the exponential stability for a class of physical ‘2 by 2’ hyperbolic systems with nonuniform steady states....

Euler equation | Stability | Lyapunov | Partial differential equation | Hyperbolic | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FEEDBACK STABILIZATION | CLASSICAL-SOLUTIONS | GAS-FLOW | AUTOMATION & CONTROL SYSTEMS | Fluid dynamics | Analysis | Differential equations

Euler equation | Stability | Lyapunov | Partial differential equation | Hyperbolic | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FEEDBACK STABILIZATION | CLASSICAL-SOLUTIONS | GAS-FLOW | AUTOMATION & CONTROL SYSTEMS | Fluid dynamics | Analysis | Differential equations

Journal Article

Mechanical Systems and Signal Processing, ISSN 0888-3270, 02/2016, Volume 68-69, pp. 155 - 175

In this paper, explicit expressions of the steady-state responses of a cracked Euler-Bernoulli beam submitted to a harmonic force are presented. The mechanical...

Forced vibration | Greens function | Cracked beam | Euler-Bernoulli beam | STEPPED BEAMS | FATIGUE CRACKS | CLOSED-FORM SOLUTION | TIMOSHENKO BEAMS | Green's function | FORMULATION | NATURAL FREQUENCIES | ENGINEERING, MECHANICAL | Analysis | Vibration | Numerical analysis | Dynamic response | Cracks | Beams (radiation) | Green's functions | Mathematical analysis | Mechanical properties | Mathematical models | Euler-Bernoulli beams

Forced vibration | Greens function | Cracked beam | Euler-Bernoulli beam | STEPPED BEAMS | FATIGUE CRACKS | CLOSED-FORM SOLUTION | TIMOSHENKO BEAMS | Green's function | FORMULATION | NATURAL FREQUENCIES | ENGINEERING, MECHANICAL | Analysis | Vibration | Numerical analysis | Dynamic response | Cracks | Beams (radiation) | Green's functions | Mathematical analysis | Mechanical properties | Mathematical models | Euler-Bernoulli beams

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 2/2018, Volume 45, Issue 2, pp. 451 - 473

This article is devoted to the elliptic Stark conjecture formulated by Darmon (Forum Math Pi 3:e8, 2015), which proposes a formula for the transcendental part...

Functions of a Complex Variable | Elliptic units | 11G05 | 11G16 | Birch and Swinnerton-Dyer conjecture | Field Theory and Polynomials | Mathematics | 11G40 | 11F67 | 11F33 | Special values | Fourier Analysis | Elliptic curves | Number Theory | p-Adic modular forms | Combinatorics | ELLIPTIC-CURVES | RATIONAL-POINTS | ZETA-FUNCTIONS | BEILINSON-FLACH ELEMENTS | SWINNERTON-DYER | MODULAR-FORMS | MATHEMATICS | EULER SYSTEMS I | COMPLEX MULTIPLICATION | HEEGNER POINTS | L-SERIES | Mathematics - Number Theory | Teoria de grups | Grups discontinus | Aritmètic | Classificació AMS | Arithmetical algebraic geometry | Teoria de nombres | Geometria algèbrica | Àlgebra | Discontinuous groups | Matemàtiques i estadística | 11 Number theory | 11G Arithmetic algebraic geometry (Diophantine geometry) | 11F Discontinuous groups and automorphic forms | Àrees temàtiques de la UPC

Functions of a Complex Variable | Elliptic units | 11G05 | 11G16 | Birch and Swinnerton-Dyer conjecture | Field Theory and Polynomials | Mathematics | 11G40 | 11F67 | 11F33 | Special values | Fourier Analysis | Elliptic curves | Number Theory | p-Adic modular forms | Combinatorics | ELLIPTIC-CURVES | RATIONAL-POINTS | ZETA-FUNCTIONS | BEILINSON-FLACH ELEMENTS | SWINNERTON-DYER | MODULAR-FORMS | MATHEMATICS | EULER SYSTEMS I | COMPLEX MULTIPLICATION | HEEGNER POINTS | L-SERIES | Mathematics - Number Theory | Teoria de grups | Grups discontinus | Aritmètic | Classificació AMS | Arithmetical algebraic geometry | Teoria de nombres | Geometria algèbrica | Àlgebra | Discontinuous groups | Matemàtiques i estadística | 11 Number theory | 11G Arithmetic algebraic geometry (Diophantine geometry) | 11F Discontinuous groups and automorphic forms | Àrees temàtiques de la UPC

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2018, Volume 463, Issue 1, pp. 398 - 411

The Mellin transform and several Dirichlet series related with the Riemann zeta function are used to deduce some identities similar to the classical Müntz...

Riemann zeta function | Müntz-type formulas | Dirichlet series | Arithmetic functions | Euler gamma function | Mellin transform | MATHEMATICS | MATHEMATICS, APPLIED | Miintz-type formulas

Riemann zeta function | Müntz-type formulas | Dirichlet series | Arithmetic functions | Euler gamma function | Mellin transform | MATHEMATICS | MATHEMATICS, APPLIED | Miintz-type formulas

Journal Article

15.
Full Text
Certain summation formulas involving harmonic numbers and generalized harmonic numbers

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 3, pp. 734 - 740

Harmonic numbers and generalized harmonic numbers have been studied since the distant past and involved in a wide range of diverse fields such as analysis of...

Stirling numbers of the first kind | Harmonic numbers | Summation formulas for pFq | Polygamma functions | Generalized harmonic numbers | Psi-function | Riemann Zeta function | Generalized hypergeometric function pFq | Hurwitz Zeta function | Summation formulas for | Generalized hypergeometric function | GAMMA | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | Riemann Zeta function, Hurwitz Zeta function | ZETA-FUNCTION | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | EULER | Statistics | Analysis | Algorithms | Hypergeometric functions | Harmonics | Mathematical analysis | Infinite series | Elementary particles | Mathematical models | Number theory

Stirling numbers of the first kind | Harmonic numbers | Summation formulas for pFq | Polygamma functions | Generalized harmonic numbers | Psi-function | Riemann Zeta function | Generalized hypergeometric function pFq | Hurwitz Zeta function | Summation formulas for | Generalized hypergeometric function | GAMMA | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | Riemann Zeta function, Hurwitz Zeta function | ZETA-FUNCTION | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | EULER | Statistics | Analysis | Algorithms | Hypergeometric functions | Harmonics | Mathematical analysis | Infinite series | Elementary particles | Mathematical models | Number theory

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 6

The objective of this paper is to derive the symmetric property of an -zeta function with weight α. By using this property, we give some interesting identities...

p -adic q -integral on | zeta function with weight α | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Genocchi numbers and polynomials with weight α | P-adic q-integral on Zp | (h q)-zeta function with weight | (h q)-Genocchi numbers and polynomials with weight | Q-EULER POLYNOMIALS | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | Q-BERNSTEIN POLYNOMIALS | NUMBERS | IDENTITIES | ANALOG | (h, q)-Genocchi numbers and polynomials with weight alpha | (h, q)-zeta function with weight alpha | p-adic q-integral on Z(p) | Z(P) | Inequalities | Mathematics - Number Theory

p -adic q -integral on | zeta function with weight α | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Genocchi numbers and polynomials with weight α | P-adic q-integral on Zp | (h q)-zeta function with weight | (h q)-Genocchi numbers and polynomials with weight | Q-EULER POLYNOMIALS | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | Q-BERNSTEIN POLYNOMIALS | NUMBERS | IDENTITIES | ANALOG | (h, q)-Genocchi numbers and polynomials with weight alpha | (h, q)-zeta function with weight alpha | p-adic q-integral on Z(p) | Z(P) | Inequalities | Mathematics - Number Theory

Journal Article

Applied Acoustics, ISSN 0003-682X, 05/2019, Volume 148, pp. 484 - 494

An analytical solution for determining the behavior of the multi-span cracked beam under concentrated load is presented. In this paper, the analytical approach...

Multi cracked beam | Euler–Bernoulli beam | Dynamic Green Function | Forced vibration | Multi-span beam | ACOUSTICS | SUPPORTED BEAMS | FREQUENCY | MASS | SUBJECT | IDENTIFICATION | DAMAGE | Euler-Bernoulli beam | Usage | Analysis | Vibration

Multi cracked beam | Euler–Bernoulli beam | Dynamic Green Function | Forced vibration | Multi-span beam | ACOUSTICS | SUPPORTED BEAMS | FREQUENCY | MASS | SUBJECT | IDENTIFICATION | DAMAGE | Euler-Bernoulli beam | Usage | Analysis | Vibration

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

Journal of Number Theory, ISSN 0022-314X, 04/2020, Volume 209, pp. 347 - 358

We deal with various Diophantine equations involving the Euler totient function and various sequences of numbers, including factorials, powers, and Fibonacci...

Euler totient function | Diophantine equations | Fibonacci sequences | Integer sequences | MATHEMATICS | FIBONACCI | LUCAS

Euler totient function | Diophantine equations | Fibonacci sequences | Integer sequences | MATHEMATICS | FIBONACCI | LUCAS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 09/2019, Volume 202, pp. 278 - 297

We obtain reasonably tight upper and lower bounds on the sum ∑n⩽xφ(⌊x/n⌋), involving the Euler functions φ and the integer parts ⌊x/n⌋ of the reciprocals of...

Euler function | Exponent pair | Reciprocals | Integer part

Euler function | Exponent pair | Reciprocals | Integer part

Journal Article