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

2016/06/11 by Bhayo, Barkat Ali, Yin, Li
#33B99 #33C99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.03621

Abstract

Motivated by the work of Alzer and Richards \citear, here authors study the monotonicity and convexity properties of the function Δ_p,q (r) = \fracE_p,q(r) - ( r' )^p K_p,q(r) r^p - \fracE'_p,q(r) - r^p K'_p,q(r) ( r' )^p , where K_p,q and E_p,q denote the complete (p,q)- elliptic integrals of the first and the second kind, respectively.

Related

• Convexity and monotonicity for the elliptic integrals of the first kind and applications
• Absolutely monotonic functions related to the asymptotic formula for the complete elliptic integral of the first kind
• On generalized complete (p,q)-elliptic integrals
• Sharp double inequality for complete elliptic integral of the first kind
• Generalized elliptic integrals