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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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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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
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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