ON GENERALIZED COMPLETE (p,q)-ELLIPTIC INTEGRALS

doi:10.1007/s10473-021-0211-4

Abstract

Abstract: In this paper, we study the generalized complete (p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters, and establish the monotonicity, generalized convexity and concavity of these functions. In particular, some Tur\'an type inequalities are given. Finally, we also show some new series representations of these functions by applying Alzer and Richard's methods.

Key words: Generalized elliptic integrals, generalized trigonometric functions, Turán type inequalities

CLC Number:

33C99

Li YIN, Barkat Ali BHAYO, Nihat Gökhan GÖĞüŞ. ON GENERALIZED COMPLETE (p,q)-ELLIPTIC INTEGRALS[J].Acta mathematica scientia,Series B, 2021, 41(2): 475-486.

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References

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