Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bex6)

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=-31/8, b>=a

For fixed z and a=-31/8, b=-9/8

http://functions.wolfram.com/07.23.03.bex6.01

Input Form

Hypergeometric2F1[-(31/8), -(9/8), 7/2, z] == (1/(1209551343 z^(5/2))) (64 (Sqrt[z] (2852 - 43493 z + 19512520 z^2 + 25981282 z^3 + 1544192 z^4 - 149669 z^5 + 10556 z^6) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-11408 + 181815 z - 2571791 z^2 - 5731310 z^3 + 6659378 z^4 + 1617707 z^5 - 154947 z^6 + 10556 z^7) 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]