Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8q8)

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=-41/8, b>=a

For fixed z and a=-41/8, b=-29/8

http://functions.wolfram.com/07.23.03.b8q8.01

Input Form

Hypergeometric2F1[-(41/8), -(29/8), 19/4, z] == (8 2^(3/4) (-261580 + 6176855 z - 88158405 z^2 + 65962734107 z^3 + 278188905191 z^4 + 293299013493 z^5 + 89635002849 z^6 + 6173507673 z^7 - 12580983 z^8 + (1/Sqrt[1 - z]) (261580 - 6307645 z + 91214135 z^2 + 63018484747 z^3 + 170716197675 z^4 - 28583900859 z^5 - 159107056059 z^6 - 44606594631 z^7 - 1539073587 z^8 + 16774644 z^9)))/ (1032196338387 (1 + Sqrt[1 - z])^(3/4) z^3)

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]