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arXiv · 1606.03621

On a function involving generalized complete $(p,q)$- elliptic integrals

Barkat Ali Bhayo·Li Yin
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Abstract

Motivated by the work of Alzer and Richards \cite{ar}, here authors study the monotonicity and convexity properties of the function $$Δ_{p,q} (r) = \frac{{E_{p,q}(r) - \left( {r'} \right)^p K_{p,q}(r) }}{r^p } - \frac{{E'_{p,q}(r) - r^p K'_{p,q}(r) }}{{\left( {r'} \right)^p }},$$ where $K_{p,q}$ and $E_{p,q}$ denote the complete $(p,q)$- elliptic integrals of the first and the second kind, respectively.

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Barkat Ali Bhayo, Li Yin. 2018-12-24. On a function involving generalized complete $(p,q)$- elliptic integrals. https://arxiv.org/abs/1606.03621

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