Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c5fc)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=15/8, b>=a

For fixed z and a=15/8, b=35/8

http://functions.wolfram.com/07.23.03.c5fc.01

Input Form

Hypergeometric2F1[15/8, 35/8, -(21/4), z] == (-127296 + 1623024 z - 9843912 z^2 + 38547027 z^3 - 114896523 z^4 + 322198338 z^5 - 2229541182 z^6 - 1478109721 z^7 - 6171935 z^8 + 292740 z^9 + (1/Sqrt[1 - z]) (-127296 + 1686672 z - 10639512 z^2 + 43274061 z^3 - 133036014 z^4 + 375383547 z^5 - 2378344716 z^6 - 2365577357 z^7 - 175497630 z^8 + 8562645 z^9 - 390320 z^10))/ (127296 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + z)^11)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]