Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4v3)

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=-17/8

http://functions.wolfram.com/07.23.03.b4v3.01

Input Form

Hypergeometric2F1[-(47/8), -(17/8), 5/2, z] == (1/(1614559485 z^(3/2))) (16 ((-Sqrt[z]) (33511 - 102696523 z - 531027850 z^2 - 441037358 z^3 - 23285405 z^4 + 2516417 z^5 - 282576 z^6 + 17864 z^7) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) (4 (-33511 + 1809594 z + 22729754 z^2 + 12730491 z^3 - 31704433 z^4 - 6127352 z^5 + 663868 z^6 - 72877 z^7 + 4466 z^8) 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]