Duplication inequalities for the ratios of hypergeometric functions

: Qiu S., Vuorinen M.

: 2000

: Forum Mathematicum

: 12

: 1

: 109

: 133

: 0933-7741

: http://api.elsevier.com/content/abstract/scopus_id:0034424376

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.