Abstract
We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it to derive the infinite sum of the Incomplete gamma function in terms of the Hurwitz zeta function. We then evaluate this formula to derive new series in terms of special functions and fundamental constants. All the results in this work are new.
Funder
Natural Sciences and Engineering Research Council of Canada
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference18 articles.
1. Einige Eigenschaften der Dirichletschen Functionen F(s) = ∑(Dn)·1n, die bei der Bestimmung der Klassenanzahlen binärer quadratischer Formen auftreten;Hurwitz;Zeitschrift Math. Phys.,1882
2. NIST Digital Library of Mathematical Functions,2010
3. Some integral and asymptotic formulas associated with the Hurwitz Zeta function
4. Contributions to the theory of the Hurwitz zeta-function;Kanemitsu;Hardy-Ramanujan J. Hardy-Ramanujan Soc.,2007
5. Crandall’s computation of the incomplete Gamma function and the Hurwitz zeta function, with applications to Dirichlet L-series
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献