In this paper, we show an elegant inequality involving the ratio of generalized complete elliptic integrals of the first kind and generalize an interesting result of Alzer.

We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through suitable transformation we can achieve that nome squared is small quantity, leading to fast numerical evaluations. Contrary case multiple polylogarithms, where it sufficient consider just variable transformations for evaluations more natural in combination (i.e. tra...

The paper classifies algebraic transformations of Gauss hypergeometric functions with the local exponent differences (1/2, 1/4, 1/4), (1/2, 1/3, 1/6) and (1/3, 1/3, 1/3). These form a special class of algebraic transformations of Gauss hypergeometric functions, of arbitrary high degree. The Gauss hypergeometric functions can be identified as elliptic integrals on the genus 1 curves y = x − x or...