ASYMPTOTIC EXPANSIONS FOR CERTAIN MATHEMATICAL CONSTANTS AND SPECIAL FUNCTIONS

Applicable Analysis and Discrete Mathematics

article

Chao-Ping Chen¹ 

[1] School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City 454000, Henan Province China

关键词: Asymptotic expansion;    Somos' quadratic recurrence constant;    Glaisher-Kinkelin constant;    Choi-Srivastava constants;    Barnes G-function.;   

DOI  :  10.2298/AADM180408017C

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

For fixed real b > 1 and α > 0, let S[α]b(n) = Pnk=1 bkk−α. Abel provedthat S[α]b(n) ∼ bn P∞k=0 ckn−(k+α)(n → ∞), and gave an explicit formulafor determining the coefficients ck ≡ ck(b, α) in terms of Stirling numbers ofthe second kind. We here provide a recurrence relation for determining thecoefficients ck, without Stirling numbers. We also consider asymptotic expansions concerning Somos’ quadratic recurrence constant, Glaisher-Kinkelinconstant, Choi-Srivastava constants, and the Barnes G-function.

【 授权许可】

Unknown