Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2m3)

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=9/8, b>=a

For fixed z and a=9/8, b=37/8

http://functions.wolfram.com/07.23.03.c2m3.01

Input Form

Hypergeometric2F1[9/8, 37/8, -(19/4), z] == (1/(1357664 2^(3/4) (-1 + z)^10)) ((1 + Sqrt[1 - z])^(3/4) (678832 - 7404628 z + 37815855 z^2 - 123027947 z^3 + 306955430 z^4 + 8038476774 z^5 + 148420219 z^6 - 20944375 z^7 + 1608528 z^8 + (1/Sqrt[1 - z]) (678832 - 7744044 z + 41433315 z^2 - 141052723 z^3 + 364178694 z^4 - 9863538066 z^5 - 1764789793 z^6 + 221675265 z^7 - 29757768 z^8 + 2144704 z^9)))

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]