Refereed journal article or data article (A1)
Landen Inequalities for Zero-Balanced Hypergeometric Functions
List of Authors: Simic S, Vuorinen M
Publisher: HINDAWI PUBLISHING CORPORATION
Publication year: 2012
Journal: Abstract and Applied Analysis
Journal name in source: ABSTRACT AND APPLIED ANALYSIS
Journal acronym: ABSTR APPL ANAL
Article number: 93261
Number of pages: 11
ISSN: 1085-3375
DOI: http://dx.doi.org/10.1155/2012/932061
Abstract
For zero-balanced Gaussian hypergeometric functions F(a, b; a + b; x), a, b > 0, we determine maximal regions of ab plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each x is an element of (0, 1). Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990.
For zero-balanced Gaussian hypergeometric functions F(a, b; a + b; x), a, b > 0, we determine maximal regions of ab plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each x is an element of (0, 1). Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990.
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