A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Infinite products and normalized quotients of hypergeometric functions
Tekijät: Qui S., Vuorinen M.
Julkaisuvuosi: 1999
Lehti:: SIAM Journal on Mathematical Analysis
Tietokannassa oleva lehden nimi: SIAM Journal on Mathematical Analysis
Vuosikerta: 30
Numero: 5
Aloitussivu: 1057
Lopetussivu: 1075
ISSN: 0036-1410
Verkko-osoite: http://api.elsevier.com/content/abstract/scopus_id:0038932568
Tiivistelmä
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).
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).
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