Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4575)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-17/3, b>=a

For fixed z and a=-17/3, b=-13/3

http://functions.wolfram.com/07.23.03.4575.01

Input Form

Hypergeometric2F1[-(17/3), -(13/3), 3/2, z] == (1/72679655) (3 (-((1/Sqrt[1 - z]) ((-23003213 - 310644285 z - 555120102 z^2 + 305783776 z^3 + 503152080 z^4 + 79660992 z^5 + 170752 z^6) Cos[ArcSin[Sqrt[z]]/3])) + (1/Sqrt[z]) ((3670016 + 226645359 z + 1565487174 z^2 + 2620643552 z^3 + 1193419632 z^4 + 115518912 z^5 - 170752 z^6) Sin[ArcSin[Sqrt[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]