Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.by1g)

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=1/8, b>=a

For fixed z and a=1/8, b=39/8

http://functions.wolfram.com/07.23.03.by1g.01

Input Form

Hypergeometric2F1[1/8, 39/8, -(11/2), z] == (1/(224874496 (1 - z)^(21/2))) (Sqrt[1 - z] (224874496 - 2280687360 z + 10455546080 z^2 - 28617044291 z^3 + 52143970887 z^4 - 67537768514 z^5 + 73100431950 z^6 - 35405282055 z^7 + 12417162667 z^8 - 2650812164 z^9 + 257777520 z^10) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (56218624 - 587740160 z + 2784598684 z^2 - 7899725567 z^3 + 14965740947 z^4 - 20182749826 z^5 + 89406533970 z^6 - 41298622963 z^7 + 13710346559 z^8 - 2779700924 z^9 + 257777520 z^10) 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]