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15. hyper geometric functions

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15. Hypergeometric Functions F m z OBERHETTINGEB Contents Mathematical properties . . . . . . . . . . . . . . . . . . . . 15.1. G a w Series, Special Elementary Cases, Special Values of the.Argument. . . . . . . . . . . . . . . . . . . . 15.2. DifferentiationFormdaa an d Gauss’ Rel ations for contiguous Functions. . . . . . . . . . . . . . . . . . . . . . 15.3. Integral Representations a n d Transformation F6rmulas . . . 15.4. Special cases o f F(u, b; c; z), Polynomials a n d Functions. . . . . . . . . . . . . . . . . . . . . . 15.5. T h e Hypergeometric Differen t ial Equat ion . . . . . . . . 15.6. Riemann’ s Differential Equation . . . . . . . . . . . . 15 .7 . Asympt otic Exp ansions . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . page 55 6 556 557 55 8 561 562 56 4 565 565 1 National Bureau o f Stcmdarda. (Presently, Or e g o n State Univemity, Corvallis, Oregon.) 66 6

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