Results 31 to 40 of about 11,866,753 (228)

Double Integral Involving Logarithmic and Quotient Function with Powers Expressed in terms of the Lerch Function

European Journal of Pure and Applied Mathematics, 2021
In this work the authors use their contour integral method to derive the double integral given by $\int_{0}^{\infty}\int_{0}^{\infty}\frac{x^{m-1} y^{m+\frac{q}{2}-1} \log ^k(a x y)}{\left(x^q+1\right)^2 \left(y^q+1\right)^2}dxdy$ in terms of the Lerch ...
Robert Reynolds, Allan Stauffer
semanticscholar   +1 more source

A note on the zeros of the Lerch zeta-function

Lietuvos Matematikos Rinkinys, 2001
In the paper we obtain the effective zero free regions for the Lerch zeta-function.
Ramūnas Garunkštis
doaj   +3 more sources

Definite Integral of Logarithmic Power and Square Root Algebraic Functions Expressed in terms of the Lerch Function

European Journal of Pure and Applied Mathematics, 2021
A definite integral involving the power square root of an algebraic function is derived in terms of the Lerch function. A table consisting of mostly new results is given for easy reading. The majority of the results in this work are new.
Robert Reynolds, Allan Stauffer
semanticscholar   +1 more source

The Lerch zeta function I. Zeta integrals [PDF]

Forum Mathematicum, 2012
Abstract. This is the first of four papers that study algebraic and analytic structures associated to the Lerch zeta function. This paper studies “zeta integrals” associated to the Lerch zeta function using test functions, and obtains functional equations for them.
Lagarias, Jeffrey C., Li, Wen-Ching Winnie   +1 more
openaire   +2 more sources

The Logarithmic Transform of a Polynomial Function Expressed in Terms of the Lerch Function

Mathematics, 2021
This is a collection of definite integrals involving the logarithmic and polynomial functions in terms of special functions and fundamental constants. All the results in this work are new.
Robert Reynolds, Allan Stauffer
semanticscholar   +1 more source

Definite integral of a hyperbolic quotient function expressed in terms of the Lerch function

European Journal of Pure and Applied Mathematics, 2021
In applied sciences it is always useful to improve the catalogue of definite integrals available in tables. In this paper the authors derived definite integrals used in research concerned with perturbation analysis of single Langmuir solitons, proving ...
Robert Reynolds, Allan Stauffer
semanticscholar   +1 more source

Subordination Properties of Meromorphic Kummer Function Correlated with Hurwitz–Lerch Zeta-Function

Mathematics, 2021
Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics.
Firas Ghanim, Khalifa Al-Shaqsi, Maslina Darus, Hiba Fawzi Al-Janaby   +3 more
doaj   +1 more source

The Mellin Transform of Logarithmic and Rational Quotient Function in terms of the Lerch Function

Journal of mathematics, 2021
Upon reading the famous book on integral transforms volume II by Erdeyli et al., we encounter a formula which we use to derive a Mellin transform given by
Robert Reynolds, Allan Stauffer
semanticscholar   +1 more source

The Lerch zeta function II. Analytic continuation [PDF]

Forum Mathematicum, 2012
Abstract. This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. The Lerch zeta function (
Lagarias, Jeffrey C., Li, Wen-Ching Winnie   +1 more
openaire   +2 more sources

A NEW EXTENSION OF THE HURWITZ- LERCH ZETA FUNCTION AND PROPERTIES USING THE EXTENDED BETA FUNCTION \(B_{p,q}^{(ρ,σ,τ)}(x,y)\)

مجلّة جامعة عدن للعلوم الأساسيّة والتّطبيقيّة, 2020
The purpose of present paper is to introduce a new extension of Hurwitz-Lerch Zeta function by using the extended Beta function. Some recurrence relations, generating relations and integral representations are derived for that new extension.
Salem Saleh Barahmah
doaj   +1 more source