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The Summation of One Class of Infinite Series

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DOI: 10.4236/am.2014.517269    5,408 Downloads   6,039 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

References

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