Some two-sided inequalities for multiple Gamma functions and related results

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• 作者：Junesang Choi^a ; ^{junesang@mail.dongguk.ac.kr} ; H.M. Srivastava^b ; ^{harimsri@math.uvic.ca}
• 关键词：Gamma ; Psi (or Digamma) and Polygamma functions ; Double and multiple Gamma functions ; Riemann and Hurwitz (or generalized) Zeta functions ; Bohr&ndash ; Mollerup theorem ; Harmonic numbers and the Stirling numbers of the first kind ; Euler&ndash ; Mascheroni and
• 刊名：Applied Mathematics and Computation
• 出版年：2013
• 出版时间：15 June, 2013
• 年：2013
• 卷：219
• 期：20
• 页码：10343-10354
• 全文大小：299 K

文摘

There is an abundant literature on inequalities for the (Euler¡¯s) Gamma function ¦£ and its various related functions. Yet, only very recently, several authors began to study inequalities for the (Barnes¡¯) double Gamma function . Here, in this paper, we aim at presenting several two-sided inequalities for the multiple Gamma functions . In our investigation of these two-sided inequalities for the multiple Gamma functions , we employ and extend a method based upon Taylor¡¯s formula and express as series involving the Zeta functions. We also give a more convenient explicit form of the multiple Gamma functions being the set of positive integers. The main two-sided inequalities for the multiple Gamma functions (which we have presented in this paper) are presumably new and their derivations provide a fruitful insight into the corresponding problem for the multiple Gamma functions when .