Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5m8)

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=37/8

http://functions.wolfram.com/07.23.03.b5m8.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, 5/4, z] == (1/(24760925 z)) (2^(1/4) (1 + Sqrt[1 - z])^(3/4) (5730381 - 199625953 z + 1516114564 z^2 - 4632634368 z^3 + 6758671360 z^4 - 4718264320 z^5 + 1270087680 z^6 + (1/Sqrt[1 - z]) (-5730381 + 214871606 z - 1888200441 z^2 + 7088528400 z^3 - 13693956864 z^4 + 14328545280 z^5 - 7737507840 z^6 + 1693450240 z^7)))

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]