Monotonicity and convexity involving generalized elliptic integral of the first kind

In this paper, we present the monotonicity properties of the ratio between generalized elliptic integral of the first kind K a ( r ) and its approximation log [ 1 + 2 / ( a r ′ ) ] , and also the convexity (concavity) of their difference for a ∈ ( 0 , 1 / 2 ] . As an application, we give new bounds...

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Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 115; no. 2
Main Authors Zhao, Tie-Hong, Wang, Miao-Kun, Chu, Yu-Ming
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Concavity
Convexity
Integrals
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
Upper bounds
Ramanujan constant
Generalized elliptic integral
Convexity
33E05
Monotonicity
33C05
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Summary:In this paper, we present the monotonicity properties of the ratio between generalized elliptic integral of the first kind K a ( r ) and its approximation log [ 1 + 2 / ( a r ′ ) ] , and also the convexity (concavity) of their difference for a ∈ ( 0 , 1 / 2 ] . As an application, we give new bounds for generalized Grötzsch ring function μ a ( r ) and a upper bound for K a ( r ) .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-020-00992-3