Sharp double-exponent type bounds for the lemniscate sine function

Abstract

In this paper, we will establish sharp inequalities of the lemniscate sine function and the so-called weighted (p,q)-exponential type function, of which the latter is an extension of the weighted H?lder mean. These results provide a systematic method for the previous obtained inequalities and give great improvements for bounds of the lemniscate sine function. As applications, several high accuracy approximations for the lemniscate sine function are also derived.