Osaka Journal of Mathematics, ISSN 0030-6126, 06/2011, Volume 48, Issue 2, pp. 291 - 309

We extend the Genocchi polynomials and investigate their Fourier expansions and integral representations. We obtain their formulas at rational arguments in...

MATHEMATICS | APOSTOL-EULER POLYNOMIALS | BERNOULLI | 11B83 | 42A16 | 33E20 | 11M35 | 33C05

MATHEMATICS | APOSTOL-EULER POLYNOMIALS | BERNOULLI | 11B83 | 42A16 | 33E20 | 11M35 | 33C05

Journal Article

The Rocky Mountain journal of mathematics, ISSN 0035-7596, 1/2014, Volume 44, Issue 2, pp. 443 - 477

The Stieltjes constants 𝛾𝑘(𝑎) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function ζ(𝑠, 𝑎) about 𝑠 = 1....

Dirichlet L functions | Stirling numbers of the first kind | Stieltjes constants | Lerch zeta function | Riemann zeta function | Laurent expansion | Hurwitz zeta function | MATHEMATICS | ZETA-FUNCTION | RIEMANN-XI FUNCTION | 11M35 | 05A10 | 11Y60 | 11M06

Dirichlet L functions | Stirling numbers of the first kind | Stieltjes constants | Lerch zeta function | Riemann zeta function | Laurent expansion | Hurwitz zeta function | MATHEMATICS | ZETA-FUNCTION | RIEMANN-XI FUNCTION | 11M35 | 05A10 | 11Y60 | 11M06

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 10/2019, Volume 30, Issue 10, pp. 844 - 855

In Ferreira and López [Asymptotic expansions of the Hurwitz-Lerch zeta function. J Math Anal Appl. 2004;298(1):210-224], the authors derived an asymptotic...

Hurwitz-Lerch zeta function | asymptotic expansion | special functions | 11M35 | Hurwitz–Lerch zeta function | MATHEMATICS | MATHEMATICS, APPLIED | Asymptotic series | Estimating techniques | Mathematics - Complex Variables

Hurwitz-Lerch zeta function | asymptotic expansion | special functions | 11M35 | Hurwitz–Lerch zeta function | MATHEMATICS | MATHEMATICS, APPLIED | Asymptotic series | Estimating techniques | Mathematics - Complex Variables

Journal Article

The Ramanujan journal, ISSN 1572-9303, 2008, Volume 16, Issue 3, pp. 247 - 270

The two-fold aim of the paper is to unify and generalize on the one hand the double integrals of Beukers for ζ(2) and ζ(3), and of the second author for...

33B15 | Functions of a Complex Variable | 11M35 | Field Theory and Polynomials | Double integral | Mathematics | Polylogarithm | Fourier Analysis | Zeta function | 11Y60 | 33B30 | 11M06 | Number Theory | Lerch transcendent | Infinite product | Combinatorics | MATHEMATICS | EULERS CONSTANT | SERIES | polylogarithm | infinite product | zeta function | double integral

33B15 | Functions of a Complex Variable | 11M35 | Field Theory and Polynomials | Double integral | Mathematics | Polylogarithm | Fourier Analysis | Zeta function | 11Y60 | 33B30 | 11M06 | Number Theory | Lerch transcendent | Infinite product | Combinatorics | MATHEMATICS | EULERS CONSTANT | SERIES | polylogarithm | infinite product | zeta function | double integral

Journal Article

Michigan Mathematical Journal, ISSN 0026-2285, 05/2018, Volume 67, Issue 2, pp. 267 - 287

In this article, we derive meromorphic continuation of multiple Lerch zeta functions by generalizing an elegant identity of Ramanujan. Further, we describe the...

MATHEMATICS | ANALYTIC CONTINUATION

MATHEMATICS | ANALYTIC CONTINUATION

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 10/2017, Volume 184, Issue 2, pp. 217 - 243

The goal of this paper is the study of a transformation concerning the general K-fold finite sums of the form $$\begin{aligned} \sum _{N\ge n_1\ge \cdots \ge...

Parametric infinite series | 11M32 | 11M35 | Mathematics, general | Mathematics | Multiple zeta-star values | Sum formula | MATHEMATICS | CYCLIC SUM | VALUES

Parametric infinite series | 11M32 | 11M35 | Mathematics, general | Mathematics | Multiple zeta-star values | Sum formula | MATHEMATICS | CYCLIC SUM | VALUES

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 2/2018, Volume 154, Issue 1, pp. 134 - 146

We provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence...

differential equation | hypergeometric Bernoulli number and polynomial | Appell polynomial | recurrence formula | Mathematics, general | Mathematics | sum of products | secondary 11B68 | primary 11M35 | MATHEMATICS | PRODUCTS | CONVOLUTION IDENTITIES | SUMS

differential equation | hypergeometric Bernoulli number and polynomial | Appell polynomial | recurrence formula | Mathematics, general | Mathematics | sum of products | secondary 11B68 | primary 11M35 | MATHEMATICS | PRODUCTS | CONVOLUTION IDENTITIES | SUMS

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 3/2019, Volume 69, Issue 1, pp. 25 - 37

Let ζ(s) be the Riemann zeta-function. If t ⩾ 6.8 and σ > 1/2, then it is known that the inequality |ζ(1 − s)| > |ζ(s)| is valid except at the zeros of ζ(s)....

Ordinary Differential Equations | functional equation | zero distribution | Analysis | Convex and Discrete Geometry | 11M35 | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | Lerch zeta-function | MATHEMATICS | PROPERTY | ZEROS

Ordinary Differential Equations | functional equation | zero distribution | Analysis | Convex and Discrete Geometry | 11M35 | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | Lerch zeta-function | MATHEMATICS | PROPERTY | ZEROS

Journal Article

Nagoya mathematical journal, ISSN 0027-7630, 2000, Volume 157, pp. 211 - 227

The joint universality theorem for Lerch zeta-functions L(λl, αl, s) (1 ≤ l ≤ n) is proved, in the case when λls are rational numbers and αls are...

MATHEMATICS | 11M35

MATHEMATICS | 11M35

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 8/2015, Volume 280, Issue 3, pp. 1085 - 1092

In this paper, we introduce the normalized Shintani L-function of several variables by an integral representation and prove its functional equation. The...

Shintani L-function | Hurwitz-Lerch zeta function | 11M32 | 11M35 | Functional equation | Mathematics, general | Mathematics | L-function | MATHEMATICS | ZETA-FUNCTIONS

Shintani L-function | Hurwitz-Lerch zeta function | 11M32 | 11M35 | Functional equation | Mathematics, general | Mathematics | L-function | MATHEMATICS | ZETA-FUNCTIONS

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2014, Volume 66, Issue 4, pp. 1105 - 1126

Let 0 < alpha < 1 be a transcendental real number and lambda(1),...,lambda(r) be real numbers with 0 <= lambda(j) < 1. It is conjectured that a joint...

Lerch zeta function | Joint universality theorem | Discrepancy | MATHEMATICS | discrepancy | joint universality theorem

Lerch zeta function | Joint universality theorem | Discrepancy | MATHEMATICS | discrepancy | joint universality theorem

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 9

We construct sequences of finite sums ( l ˜ n ) n ≥ 0 $(\tilde{l}_{n})_{n\geq 0}$ and ( u ˜ n ) n ≥ 0 $(\tilde{u}_{n})_{n\geq 0}$ converging increasingly and...

alternating zeta function | Euler-Mascheroni constant | Analysis | 11M35 | infinite product | Mathematics, general | Mathematics | Applications of Mathematics | gamma process | fast computation | 33F05 | 60E05 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | MASCHERONI CONSTANT | Differentiation | Convergence | Research

alternating zeta function | Euler-Mascheroni constant | Analysis | 11M35 | infinite product | Mathematics, general | Mathematics | Applications of Mathematics | gamma process | fast computation | 33F05 | 60E05 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | MASCHERONI CONSTANT | Differentiation | Convergence | Research

Journal Article

Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 12/2015, Volume 53, Issue 2, pp. 305 - 311

Funct. Approx. Comment. Math. Volume 53, Number 2 (2015), 305-311 Expressions for a family of integrals involving the Hurwitz zeta function are established...

Fourier integrals | Hurwitz zeta function | Mathematics - Number Theory | 42A38 | 11M35

Fourier integrals | Hurwitz zeta function | Mathematics - Number Theory | 42A38 | 11M35

Journal Article

Forum Mathematicum, ISSN 0933-7741, 03/2015, Volume 27, Issue 2, pp. 929 - 936

Let be positive integers and define the multiple -values of depth by which is equal to the multiple Hurwitz-zeta value where is called the weight. For , let be...

symmetric functions | Multiple Hurwitz-zeta values | 11M32 | 11M35 | generating functions | multiple zeta functions | recursive systems of DE | 05A15 | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Number Theory

symmetric functions | Multiple Hurwitz-zeta values | 11M32 | 11M35 | generating functions | multiple zeta functions | recursive systems of DE | 05A15 | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Number Theory

Journal Article

Numerical Algorithms, ISSN 1017-1398, 6/2015, Volume 69, Issue 2, pp. 253 - 270

We study the use of the Euler-Maclaurin formula to numerically evaluate the Hurwitz zeta function ζ(s, a) for s , a ∈ ℂ $s, a \in \mathbb {C}$ , along with an...

68W30 | 11M35 | Numeric Computing | Fast polynomial arithmetic | Theory of Computation | Power series | 33F05 | Hurwitz zeta function | 65D20 | Algorithms | Algebra | Numerical Analysis | Computer Science | Riemann zeta function | 11-04 | 11M06 | Rigorous numerical evaluation | Arbitrary-precision arithmetic | MATHEMATICS, APPLIED | FAST ALGORITHMS | POWER-SERIES | EFFICIENT ALGORITHM | STIELTJES CONSTANTS | FORMULA

68W30 | 11M35 | Numeric Computing | Fast polynomial arithmetic | Theory of Computation | Power series | 33F05 | Hurwitz zeta function | 65D20 | Algorithms | Algebra | Numerical Analysis | Computer Science | Riemann zeta function | 11-04 | 11M06 | Rigorous numerical evaluation | Arbitrary-precision arithmetic | MATHEMATICS, APPLIED | FAST ALGORITHMS | POWER-SERIES | EFFICIENT ALGORITHM | STIELTJES CONSTANTS | FORMULA

Journal Article

The Ramanujan journal, ISSN 1572-9303, 2014, Volume 38, Issue 2, pp. 331 - 347

H. Mishou proved that the Riemann zeta-function and Hurwitz zeta-function with transcendental parameter are jointly universal, i.e., their shifts (continuous)...

Functions of a Complex Variable | 11M35 | Hurwitz zeta-function | Field Theory and Polynomials | Mathematics | Joint universality | Universality | Limit theorem | Algebraically independent numbers | Fourier Analysis | 11M06 | Number Theory | Combinatorics | Riemann zeta-function | MATHEMATICS | ZETA

Functions of a Complex Variable | 11M35 | Hurwitz zeta-function | Field Theory and Polynomials | Mathematics | Joint universality | Universality | Limit theorem | Algebraically independent numbers | Fourier Analysis | 11M06 | Number Theory | Combinatorics | Riemann zeta-function | MATHEMATICS | ZETA

Journal Article

Lithuanian Mathematical Journal, ISSN 0363-1672, 1/2019, Volume 59, Issue 1, pp. 54 - 66

We investigate the mixed joint discrete value distribution and the mixed joint discrete universality for the pair consisting of a rather general form of...

joint approximation | universality | 11M41 | value distribution | 11M35 | Hurwitz zeta-function | Matsumoto zeta-function | Probability Theory and Stochastic Processes | Mathematics | Actuarial Sciences | probability measure | periodic coefficients | Steuding class | Ordinary Differential Equations | Mathematics, general | 11M06 | Number Theory | weak convergence | arithmetic progression | MATHEMATICS

joint approximation | universality | 11M41 | value distribution | 11M35 | Hurwitz zeta-function | Matsumoto zeta-function | Probability Theory and Stochastic Processes | Mathematics | Actuarial Sciences | probability measure | periodic coefficients | Steuding class | Ordinary Differential Equations | Mathematics, general | 11M06 | Number Theory | weak convergence | arithmetic progression | MATHEMATICS

Journal Article

18.
Full Text
An asymptotic series related to Ramanujan’s expansion for the $$n$$ n th Harmonic number

The Ramanujan Journal, ISSN 1382-4090, 2/2016, Volume 39, Issue 2, pp. 303 - 313

In this paper, we investigate certain asymptotic series for the tail of the Riemann Zeta function used by M. D. Hirschhorn to prove an asymptotic expansion of...

Asymptotic expansions | Fourier Analysis | Functions of a Complex Variable | Harmonic numbers | 11M35 | Field Theory and Polynomials | Mathematics | 41A60 | 11M06 | Number Theory | Combinatorics | Zeta functions

Asymptotic expansions | Fourier Analysis | Functions of a Complex Variable | Harmonic numbers | 11M35 | Field Theory and Polynomials | Mathematics | 41A60 | 11M06 | Number Theory | Combinatorics | Zeta functions

Journal Article

Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 05/2014, Volume 51, Issue 1, pp. 7 - 22

We introduce poly-Euler polynomials, which generalize Euler polynomials. Various results about them are provided. Furthermore, we introduce zeta functions of...

Euler numbers and polynomials | Zeta function | Bernoulli numbers and polynomials | Polylogarithms | 11M32 | 11M35 | zeta function | polylogarithms | 11B68

Euler numbers and polynomials | Zeta function | Bernoulli numbers and polynomials | Polylogarithms | 11M32 | 11M35 | zeta function | polylogarithms | 11B68

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 11/2016, Volume 41, Issue 1, pp. 171 - 182

We revisit the classical theorem of Euler regarding special values of the Riemann zeta function as well as Hecke’s generalization of this to Dirichlet’s $$L$$...

11J89 | Functions of a Complex Variable | 11M35 | Field Theory and Polynomials | Mathematics | Hurwitz zeta function | Special values | Fourier Analysis | Transcendence | Eisenstein series | Number Theory | Elliptic functions | Dirichlet’s $$L$$ L -series | Combinatorics | Dirichlet’s L-series | MATHEMATICS | Dirichlet's L-series

11J89 | Functions of a Complex Variable | 11M35 | Field Theory and Polynomials | Mathematics | Hurwitz zeta function | Special values | Fourier Analysis | Transcendence | Eisenstein series | Number Theory | Elliptic functions | Dirichlet’s $$L$$ L -series | Combinatorics | Dirichlet’s L-series | MATHEMATICS | Dirichlet's L-series

Journal Article

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