Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50916#.VFB_GFfHRK0 Author(s) Jonathan D. Weiss Affiliation(s) JSA Photonics LLC, Corrales, New Mexico, USA . 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: 2 l ∏ λ and 2 l ∏ λ , 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 prese...
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