# On Some Integrals Involving the Hurwitz Zeta Function: Part 1

@article{Espinosa2002OnSI, title={On Some Integrals Involving the Hurwitz Zeta Function: Part 1}, author={Olivier Espinosa and Victor H. Moll}, journal={The Ramanujan Journal}, year={2002}, volume={6}, pages={159-188} }

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, ln Γ(q) and ln sin(q).

## 52 Citations

Jackson’s integral of the Hurwitz zeta function

- Mathematics
- 2007

We give a Jacksonq-integral analogue of Euler’s logarithmic sine integral established in 1769 from several points of view, specifically from the one relating to the Hurwitz zeta function.

A formula for the Hurwitz zeta function, Riemann's functional equation and certain integral representations

- MathematicsTsukuba Journal of Mathematics
- 2018

There is a well-known formula for the Hurwitz zeta function which implies the functional equation for the Riemann zeta function. We give a new proof of that formula and recover certain integral…

Moment integrals of 1/sint and related zeta-values

- Mathematics
- 2014

In this paper we shall discuss the moment integrals of 1/sint as a generalization of one of the integral representations of the Catalan constant. As an application of our formulas, we shall derive…

On Some Integrals Involving the Hurwitz Zeta Function: Part 2

- Mathematics
- 2001

AbstractWe establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln…

Some applications of the Dirichlet integrals to the summation of series and the evaluation of integrals involving the Riemann zeta function

- Mathematics
- 2012

Using the Dirichlet integrals, which are employed in the theory of Fourier series, this paper develops a useful method for the summation of series and the evaluation of integrals.

Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume VI

- Mathematics
- 2007

In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some…

Integrals of inverse trigonometric and polylogarithmic functions

- Mathematics
- 2020

In this paper we study the representation of integrals whose integrand involves the product of a polylogarithm and an inverse or inverse hyperbolic trigonometric function. We further demonstrate many…

MOMENTS OF HYPERGEOMETRIC HURWITZ ZETA FUNCTIONS

- Mathematics
- 2011

This paper investigates a generalization the classical Hurwitz zeta function. It is shown that many of the properties exhibited by this special function extends to class of functions called…

Some trigonometric integrals involving the log gamma and the digamma function

- Mathematics
- 2010

This paper considers various integrals where the integrand includes the log gamma function (or its derivative, the digamma function) multiplied by a trigonometric or hyperbolic function. Some…

## References

SHOWING 1-10 OF 27 REFERENCES

On Some Integrals Involving the Hurwitz Zeta Function: Part 2

- Mathematics
- 2001

AbstractWe establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln…

A Course in Arithmetic

- Mathematics
- 1973

Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on…

APPLICATION OF THE HURWITZ ZETA FUNCTION TO THE EVALUATION OF CERTAIN INTEGRALS

- Mathematics
- 1993

Abstract The Hurwitz zeta function ζ(s, a) is defined by the series for 0 < a ≤ 1 and σ = Re(s) > 1, and can be continued analytically to the whole complex plane except for a simple pole at s = 1…

Table of Integrals, Series, and Products

- Mathematics
- 1943

Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special…

Integrals and series

- Mathematics
- 1992

The pages of this expensive but invaluable reference work are dense with formulae of stupefying complexity. Chapters 1 and 2 treat definite/indefinite integral properties of a great variety of…

On three trigonometric integrals of ln G( x ) or its derivative

- Mathematics
- 1994

Elliptic Curves: Function Theory, Geometry, Arithmetic

- Mathematics
- 1997

1. First ideas: complex manifolds, Riemann surfaces, and projective curves 2. Elliptic functions and elliptic integrals 3. Theta functions 4. Modular groups and molecular functions 5. Ikosaeder and…

Ten Physical Applications of Spectral Zeta Functions

- Mathematics
- 1995

Introduction and Outlook.- Mathematical Formulas Involving the Different Zeta Functions.- A Treatment of the Non-Polynomial Contributions: Application to Calculate Partition Functions of Strings and…