General Mathematics

    

On the Generalization of Glaisher—Kinkelin‘s Constant and Its Applications

Authors: SonHyang Ri, Il Yun, Chol Ho Ji, Hong Rok Ri

In this paper, we have found the exquisite relation between Stirling’s formula andinteresting expression for Glaisher—Kinkelin’s constant,Bendersky—Adamchik’sconstant, andhave introduced new constants astheir generalization.As we calculate the singular integral or sum of series in form of closed expression by introducingconstant π, Euler constant, Glaisher-Kinkelin’s constant,Bendersky—Adamchik’sconstant, new constantswill play important role in calculating of the sum of multi-series which has the multi-power in general term. To demonstrate the superiority of our new constants in several calculations, we propose an exampleWe show that our new constants generalize Glaisher—Kinkelin’s constant and Bendersky—Adamchik’s constant

Comments: 17 Pages.

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[v1] 2024-01-30 02:06:52

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