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New solutions to Legendre’s incomplete elliptic integrals of the first and second kinds and p-elliptic integrals

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Abstract

The elliptic integrals are of interest in various disciplines. While series solutions do exist for complete elliptic integrals, there are no deduced series solutions for Incomplete elliptic integrals, in terms of the special functions. This paper provides novel solutions of the Legendre forms of incomplete elliptic integrals of the first and second kinds in terms of the Euler’s gamma functions. The paper also proposes new solutions to inverse trigonometric functions, which has never been known till date.

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Authors and Affiliations

  1. Ponda, Goa, India

    Prateek Pralhad Kulkarni

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  1. Prateek Pralhad Kulkarni
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Correspondence to Prateek Pralhad Kulkarni.

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Prateek Koulakarnee also known as Prateek Pralhad Kulkarni.

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Kulkarni, P.P. New solutions to Legendre’s incomplete elliptic integrals of the first and second kinds and p-elliptic integrals. Ricerche mat 73, 471–479 (2024). https://doi.org/10.1007/s11587-021-00614-z

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  • DOI: https://doi.org/10.1007/s11587-021-00614-z

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