Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9v1)

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=-17/8

http://functions.wolfram.com/07.23.03.b9v1.01

Input Form

Hypergeometric2F1[-(39/8), -(17/8), 11/2, z] == (1/(151522947896925 z^(9/2))) (1024 (Sqrt[z] (319424 - 5618440 z + 52543109 z^2 - 396851522 z^3 + 152589375987 z^4 + 301187085984 z^5 + 108523113915 z^6 + 2706850662 z^7 - 125054931 z^8 + 4776996 z^9) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-1277696 + 23352176 z - 225518335 z^2 + 1730106621 z^3 - 19545947423 z^4 - 58843812639 z^5 + 31795553391 z^6 + 42421429335 z^7 + 2768781003 z^8 - 127443429 z^9 + 4776996 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]