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). 
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References

SHOWING 1-10 OF 27 REFERENCES
On Some Integrals Involving the Hurwitz Zeta Function: Part 2
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
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
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
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
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
Elliptic Curves: Function Theory, Geometry, Arithmetic
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
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
...
1
2
3
...