Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ba1f)

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=-39/8, b>=a

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

http://functions.wolfram.com/07.23.03.ba1f.01

Input Form

Hypergeometric2F1[-(39/8), -(1/8), 11/2, z] == (1/(9720340053765 z^(9/2))) (1024 (Sqrt[z] (319424 - 3907240 z + 23431319 z^2 - 99876327 z^3 + 10013302562 z^4 + 1551877754 z^5 - 389547285 z^6 + 96043157 z^7 - 16193716 z^8 + 1321936 z^9) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-1277696 + 16507376 z - 104365375 z^2 + 462709906 z^3 - 2350690413 z^4 + 588694976 z^5 + 1735606471 z^6 - 435627270 z^7 + 103974773 z^8 - 16854684 z^9 + 1321936 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]