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Some Trigonometric and Elliptic Integrals

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Abstract

Simultaneous identities involving elliptic integrals of the first and second kinds, evaluated at the roots of a very simple trigonometric polynomial, are given. There are two parameters m ∈ N, k ∈ ℝ+ and just the cases to = 1, 2, 3, 4 are treated, the remainder being offered as a problem. The identities originate in the evaluation of some trigonometric integrals which start the paper.

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References

  1. R. R. Hall, An extremal problem for polynomials, Bull. London Math. Soc. 17 (1985), 463–468.

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  2. E. T. Whittaker and G. N. Watson, Modern Analysis, Cambridge, 1927.

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Authors and Affiliations

  1. Mathematics Department, York University, Heslington, York, YO10 5DD, UK

    Richard R. Hall

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  1. Richard R. Hall
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Correspondence to Richard R. Hall.

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Hall, R.R. Some Trigonometric and Elliptic Integrals. Comput. Methods Funct. Theory 8, 531–544 (2008). https://doi.org/10.1007/BF03321703

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  • DOI: https://doi.org/10.1007/BF03321703

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