Monotonicity properties and inequalities for the generalized elliptic integral of the first kind

Huang, Ti-Ren; Qiu, Song-Liang; Ma, Xiaonan

doi:10.1016/j.jmaa.2018.08.061

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Cited by 21 publications

(2 citation statements)

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“…For more information on these and related functions, we refer the reader to [5,7,9] and, for recently obtained related results, to [8,14,15,20,22,[25][26][27]30,31] and the references contained therein.…”

Section: Introductionmentioning

confidence: 99%

Monotonicity and convexity involving generalized elliptic integral of the first kind

Zhao

Wang

Chu

2021

RACSAM

105

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Section: Introductionmentioning

confidence: 99%

Monotonicity and convexity involving generalized elliptic integral of the first kind

Zhao

Wang

Chu

2021

RACSAM

105

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“…Relatively speaking, the study of the dependence on the parameter a of K a (r) is more difficult and fewer achievements. For above, and the recent development of K a (r) and K (r), the readers can refer to the literatures [2,10,11,12,13,22,23,24,27,29].…”

Section: Introductionmentioning

confidence: 99%

A monotonicity theorem for the generalized elliptic integral of the first kind

Bao

Ren

Wang

2022

APPL ANAL DISCRETE M

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For a ? (0,1/2] and r ? (0,1), let Ka(r) (K (r)) denote the generalized elliptic integral (complete elliptic integral, respectively) of the first kind. In this article, we mainly present a sufficient and necessary condition under which the function a ? [K(r)-Ka(r)]=(1-2a)?(?? R) is monotone on (0,1/2) for each fixed r ? (0,1). The obtained result leads to the conclusion that inequality K (r)- (1-2a)? [K(r)- ?/2] ? Ka(r) ? K (r)-(1-2a)? [K(r)-?/2] holds for all a ? (0,1/2] and r ? (0,1) with the best possible constants ? = ?/2 and ? = 2.

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On the Convexity and Concavity of Generalized Complete Elliptic Integral of the First Kind

Chen

Zhao

2022

Results Math

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Monotonicity properties and inequalities for the generalized elliptic integral of the first kind

Cited by 21 publications

References 32 publications

Monotonicity and convexity involving generalized elliptic integral of the first kind

Monotonicity and convexity involving generalized elliptic integral of the first kind

A monotonicity theorem for the generalized elliptic integral of the first kind

On the Convexity and Concavity of Generalized Complete Elliptic Integral of the First Kind

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