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Precise Estimates for Differences of the Gaussian Hypergeometric Function

✍ Scribed by G.D Anderson; S.-L Qiu; M Vuorinen

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
258 KB
Volume
215
Category
Article
ISSN
0022-247X

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✦ Synopsis

By showing certain combinations of the Gaussian hypergeometric functions Ε½ c . Ε½ d . Ε½ . F a, b; a q b; 1 y x and F a y ␦, b q ␦; a q b; 1 y x to be monotone on 0, 1 Ε½ . for given a, b, c, d g 0, Ο± , a F b, and cd, the authors study the problem of Γ„ Ε½ . Ε½ c . comparing these two functions. They find sup ␦ g 0, a : F a, b; a q b; 1 y x -Ε½ d . Ε½ . 4 F a y ␦, b q ␦; a q b; 1 y x for x g 0, 1 , thus solving an open problem and a recent conjecture.

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