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

Abstract

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

11 pages

References in corpus (2)

• Complete $(p,q)$-elliptic integrals with application to a family of means
• On generalized complete $(p,q)$-elliptic integrals