Applications of the Hurwitz-Lerch Zeta-Function
Pure and Applied Mathematics Journal
Volume 4, Issue 2-1, March 2015, Pages: 30-35
Received: Nov. 5, 2014; Accepted: Nov. 14, 2014; Published: Dec. 27, 2014
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Authors
Tomihiro Arai, Grad. School of Advances Tech. Kinki Univ.,Iizuka, Japan
Kalyan Chakraborty, Harish-Chandra Institute, Allahabad, Allahabad, India
Jing Ma, Dept. of Math., Jilin Univ., Changchun, PRC
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Abstract
In this paper, we shall exhibit the use of two principles, “principle of decomposition into residue classes” and “binomial principle of analytic continuation” due to Ram Murty and Sinha and indicate a certain distribution property and the functional equation for the Lipschitz-Lerch transcendent at integral arguments ofs. By considering the limiting cases ,we can also deduce new striking identities for Lipschizt-Lerch transcendent, among which is the Gauss second formula for the digamma function, Lipschitz-Lerch transcendent
Keywords
Decomposition into Residue Classes, Binomial Expansion, Distribution Property, Zeta-Functions, Functional Equation
To cite this article
Tomihiro Arai, Kalyan Chakraborty, Jing Ma, Applications of the Hurwitz-Lerch Zeta-Function, Pure and Applied Mathematics Journal. Special Issue: Abridging over Troubled Water---Scientific Foundation of Engineering Subjects. Vol. 4, No. 2-1, 2015, pp. 30-35. doi: 10.11648/j.pamj.s.2015040201.16
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