Related papers: Bessel Integrals, Periods and Zeta Numbers

We investigate the relationship between the poles of Igusa zeta integrals and the unextendability of semi-invariant distributions. Under some algebraic conditions, we obtain an upper bound for the order of the poles of Igusa zeta integral,…

In this paper, we establish some expressions of Mneimneh-type binomial sums involving multiple harmonic-type sums in terms of finite sums of Stirling numbers, Bell numbers and some related variables. In particular, we present some new…

This paper describes some validated numerics aspects of Riemann zeta function, Dirichlet L-functions, Dedekind zeta functions and Hasse-Weil L-functions.

We present several formulae for the Selberg type integrals associated with the Lie algebra $sl_3$.

Historically known as the Basel problem, evaluating the Riemann zeta function at two has resulted in numerous proofs, many of which have been generalized to compute the function's values at even positive integers. We apply Parseval's…

Using a polylogarithmic identity, we express the values of $\zeta$ at odd integers $2n+1$ as integrals over unit $n-$dimensional hypercubes of simple functions involving products of logarithms. We also prove a useful property of those…

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…

We give an explicit representation for the sums of multiple zeta-star values of fixed weight and height in terms of Riemann zeta values.

Let $\gamma$ denote imaginary parts of complex zeros of the Riemann zeta-function $\zeta(s)$. Certain sums over the $\gamma$'s are evaluated, by using the function $G(s) = \sum_{\gamma>0}\gamma^{-s}$ and other techniques. Some integrals…

We realize that geometric polynomials and p-Bernoulli polynomials and numbers are closely related with an integral representation. Therefore, using geometric polynomials, we extend some properties of Bernoulli polynomials and numbers such…

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…

Using Bauer's expansion and properties of spherical Bessel and Legender functions, we deduce a new transform and briefly indicate its use.

Using Jacobi's identity we derive a simple expression for the Bessel functions of integer order in terms of combinations of powers and hyperbolic functions of the same argument.

By using the associated and restricted Stirling numbers of the second kind, we give some generalizations of the poly-Bernoulli numbers. We also study their arithmetical and combinatorial properties. As an application, at the end of the…

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…

Expressions for the derivatives with respect to order of modified Bessel functions evaluated at integer orders and certain integral representations of associated Legendre functions with modulus argument greater than unity are used to…

In this paper we study the higher-order Euler numbers and polynomials and we introduce the mutiple zeta functions which interpolate higher-order Euler polynomials and numbers at negative integers

We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.

We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel functions and their derivatives in terms of inverse values…

We consider the variation of two fundamental types of zeta functions that arise in the study of both physical and analytical problems in geometric settings involving conical singularities. These are the Barnes zeta functions and the Bessel…