Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4n2)

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=-41/8

http://functions.wolfram.com/07.23.03.b4n2.01

Input Form

Hypergeometric2F1[-(47/8), -(41/8), 1/2, z] == (1/(18409461 Sqrt[1 - z])) (Sqrt[1 - z] (18409461 + 1129916778 z + 7762541011 z^2 + 12963674988 z^3 + 5955845451 z^4 + 615836938 z^5 + 3739405 z^6) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (-82987011 - 1129512958 z - 2060804317 z^2 + 1063576476 z^3 + 1879495283 z^4 + 326493122 z^5 + 3739405 z^6) Sin[ArcSin[Sqrt[z]]/4])

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]