Related papers: Infinite integrals in terms of series
This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…
By employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions. We use this procedure to find special…
In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta. These derivations are then…
We show that the generalised Stieltjes constants may be represented by infinite series involving logarithmic terms. Some relations involving the derivatives of the Hurwitz zeta function are also investigated
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Gamma(q) and log sin(q).
In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour…
Various product and sum relationships are established using special functions, specifically involving Special functions. These relationships are derived from formulas inspired by the finite sum that incorporates the Hurwitz-Lerch zeta…
An extension of two finite trigonometric series is studied to derive closed form formulae involving the Hurwitz-Lerch zeta function. The trigonometric series involves angles with a geometric series involving the powers of 3. These closed…
This paper introduces a set of finite summation formulas and utilize them to establish various functional relationships involving the multivariable Hurwitz-Lerch zeta function. Additionally, the paper examines several examples of these…
The Watson-Harkins sum involving the product of the cosine and cosecant functions is extended to derive the finite sum of generalized Hurwitz-Lerch Zeta functions is derived in terms of the Hurwitz-Lerch Zeta function. A transformation…
We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.
In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.
The purpose of this article is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…
This paper considers some infinite series involving the Riemann zeta function.
We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.
We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some…
In this paper we derive two expressions for the Hurwitz zeta function involving the complete Bell polynomials in the restricted case where q is a positive integer greater than 1. The arguments of the complete Bell polynomials comprise the…
In this article it is proven the existence of integration of indefinite integrals as infinite derivative's series expansion. This also opens a new way to integrate a definite integral.
We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.