Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function
Copyright policy ) Gaboury, S.; Bayad, Abdelmejid;
Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function
By making use of some explicit relationships between the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Frobenius-Euler polynomials of higher order and the generalized Hurwitz-Lerch zeta function as well as a new expansion formula for the generalized Hurwitz-Lerch zeta function obtained recently by Gaboury and Bayad , in this paper we present some series representations for these polynomials at rational arguments. These results provide extensions of those obtained by Apostol (1951) and by Srivastava (2000).
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- Département Sciences sociales, agriculture et alimentation, espace et environnement France
- École Nationale Supérieure d’Informatique pour l’Industrie et l’Entreprise France
- University of Paris-Saclay France
- French National Centre for Scientific Research France
- National Research Institute for Agriculture, Food and Environment France
Asymptotic approximations, asymptotic expansions (steepest descent, etc.), QA1-939, Hurwitz and Lerch zeta functions, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Mathematics, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Asymptotic approximations, asymptotic expansions (steepest descent, etc.), QA1-939, Hurwitz and Lerch zeta functions, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Mathematics, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
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