Open AccessExtended Apelblat Integrals for Fractional Calculus
Author(s) -
Robert Reynolds,
A D Stauffer
Publication year - 2022
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v15i1.4181
Subject(s) - mathematics , logarithm , fractional calculus , gamma function , pure mathematics , polylogarithm , exponential function , polynomial , riemann zeta function , calculus (dental) , arithmetic zeta function , mathematical analysis , prime zeta function , medicine , dentistry
A quadruple integral involving the logarithmic, exponential, polynomial and Gamma functions is derived in terms of the Hurwitz-Lerch zeta function. Special cases of this integral are evaluated in terms of special functions and fundamental constants. Almost all Hurwitz-Lerch zeta functions have an asymmetrical zero-distribution. The majority of the results in this work are new.