Asymptotic expansions of the gamma function and Wallis function through polygamma functions

Tomislav Buri?; Neven Elezovi?; Lenka Vuk?i?

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Asymptotic expansions of the gamma function and Wallis function through polygamma functions

机译：伽玛函数和沃利斯函数通过多伽玛函数的渐近展开

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摘要

A new view on classical asymptotic expansions of the logarithm of gamma function is given. Then general formulae for the asymptotic expansions of the logarithm of gamma function and theWallis power function through polygamma functions are derived and analysed.

机译：给出了伽马函数对数的经典渐近展开的新观点。然后推导并分析了通过伽马函数对伽马函数和沃利斯幂函数的对数的渐近展开的一般公式。

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来源
《Integral transforms and special functions》 |2014年第3期|共10页
作者
Tomislav Buri?; Neven Elezovi?; Lenka Vuk?i?;
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正文语种 eng
中图分类高等数学;
关键词
asymptotic expansion; gamma function; polygamma functions; Bernoulli polynomials;

机译：渐近展开;伽马函数;多伽马函数;伯努利多项式;

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1. Asymptotic expansions of the gamma function and Wallis function through polygamma functions [J] . Tomislav Buri?, Neven Elezovi?, Lenka Vuk?i? Integral transforms and special functions . 2014,第1a3期

机译：伽玛函数和沃利斯函数通过多伽玛函数的渐近展开
2. ASYMPTOTIC EXPANSIONS OF INTEGRAL MEAN OF POLYGAMMA FUNCTIONS [J] . Chen Chao-Ping, Elezovic Neven, Vuksic Lenka Mathematical inequalities & applications . 2015,第1期

机译：聚γ函数积分均值的渐近展开
3. Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function [J] . Koumandos S., Pedersen H.L. Journal of Mathematical Analysis and Applications . 2009,第1期

机译：Barnes双伽马函数和Euler伽马函数对数的正阶完全单调函数和渐近展开
4. Complete asymptotic expansions associated with various zeta-functions [C] . Masanori Katsurada International Conference "Various Aspects of Multiple Zeta Functions" . 2020

机译：与各种Zeta功能相关的完整渐近扩展
5. Asymptotics for Orthogonal Polynomials, Exponentially Small Perturbations and Meromorphic Continuations of Herglotz Functions. [D] . Kozhan, Rostyslav. 2010

机译：正交多项式的渐近性，Herglotz函数的指数小扰动和亚纯连续。
6. Some Inequalities for the q-Analogue of the Classical Riemann Zeta Functions and the q-Polygamma Functions [O] . Banyat Sroysang -1

机译：经典Riemann Zeta函数的q-模拟和q-Polygamma函数的一些不等式
7. Asymptotic expansions of the logarithm of the gamma function in the terms of the polygamma functions [O] . Chao-Ping Chen 2014

机译：在PolyGama函数的术语中伽马函数对数的渐近扩展

Asymptotic expansions of the gamma function and Wallis function through polygamma functions

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