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 AM  Vol.5 No.17 , October 2014
The Summation of One Class of Infinite Series
Jonathan D. Weiss
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Abstract: This paper presents closed-form expressions for the series, , where the sum is from n = 1 to n = ∞. These expressions were obtained by recasting the series in a different form, followed by the use of certain relationships involving the elliptical nome. Among the values of x for which these expressions can be obtained are of the form: and , where l is an integer between –∞ and ∞. The values of λ include 1,,and 3. Examples of closed-form expressions obtained in this manner are first presented for , , , and . Additional examples are then presented for , , , and . This undertaking was prompted by the author’s work on an electrostatics boundary-value problem related to the van der Pauw measurement technique of electrical resistivity. The presence of this series for x = in the solution of that problem and its absence from any compendium of infinite series that he consulted led to this work.
Keywords: Infinite Series, Hyperbolic Functions, Elliptical Nome
Cite this paper: Weiss, J. (2014) The Summation of One Class of Infinite Series. Applied Mathematics, 5, 2815-2822. doi: 10.4236/am.2014.517269.
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