Infinite products and normalized quotients of hypergeometric functions

: Qui S., Vuorinen M.

: 1999

: SIAM Journal on Mathematical Analysis

: 30

: 5

: 1057

: 1075

: 19

: 0036-1410

: http://api.elsevier.com/content/abstract/scopus_id:0038932568

For r ∈ (0, 1) and α ∈ (0,1) the authors consider the quotient of hypergeometric functions μα(r) ≡ cF(α,1-α; 1; 1 - r)/F(α, 1 - α; 1;r), where the normalizing coefficient c = π/(2 sin(πα)). With this choice of c, μ(r) ≡ μ(r), where μ(r) is the modulus of the Grötzsch ring B \ [0, r] in the plane. A new infinite product expansion is given for μ(r). It is shown that several well-known properties of the function μ(r) have their counterparts for μα(r).