Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5qw)

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=-47/8, b>=a

For fixed z and a=-47/8, b=45/8

http://functions.wolfram.com/07.23.03.b5qw.01

Input Form

Hypergeometric2F1[-(47/8), 45/8, -(7/2), z] == (1/3845632) (-((1/(1 - Sqrt[z])^(13/4)) (-1922816 + 6249152 Sqrt[z] - 25185456 z + 61933560 z^(3/2) - 183833871 z^2 + 408761496 z^(5/2) - 1200506736 z^3 + 2680886208 z^(7/2) - 12373320960 z^4 + 17803468800 z^(9/2) + 80719921152 z^5 - 225637761024 z^(11/2) + 83381256192 z^6 + 246397009920 z^(13/2) - 277387149312 z^7 + 85349892096 z^(15/2))) + (1/(1 + Sqrt[z])^(13/4)) (1922816 + 6249152 Sqrt[z] + 25185456 z + 61933560 z^(3/2) + 183833871 z^2 + 408761496 z^(5/2) + 1200506736 z^3 + 2680886208 z^(7/2) + 12373320960 z^4 + 17803468800 z^(9/2) - 80719921152 z^5 - 225637761024 z^(11/2) - 83381256192 z^6 + 246397009920 z^(13/2) + 277387149312 z^7 + 85349892096 z^(15/2)))

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]