A1 Refereed original research article in a scientific journal
Duplication inequalities for the ratios of hypergeometric functions
Authors: Qiu S., Vuorinen M.
Publication year: 2000
Journal:: Forum Mathematicum
Journal name in source: Forum Mathematicum
Volume: 12
Issue: 1
First page : 109
Last page: 133
ISSN: 0933-7741
Web address : http://api.elsevier.com/content/abstract/scopus_id:0034424376
Abstract
The authors derive the analogs of the duplication formula and logarithmic inequalities satisfied by μ(r), the modulus of the plane Grötzsch ring B\[0, r], for its generalization μ(r) ≡ πF(a, 1 - a; 1; 1 - r)/[2F(a, 1 - a; r) sin(πa)] for a ∈ (0, 1/2] and r ∈ (0, 1). Sharp estimates are obtained for μ(r), too.
The authors derive the analogs of the duplication formula and logarithmic inequalities satisfied by μ(r), the modulus of the plane Grötzsch ring B\[0, r], for its generalization μ(r) ≡ πF(a, 1 - a; 1; 1 - r)/[2F(a, 1 - a; r) sin(πa)] for a ∈ (0, 1/2] and r ∈ (0, 1). Sharp estimates are obtained for μ(r), too.
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