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

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=-37/8, b>=a

For fixed z and a=-37/8, b=-11/8

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

Input Form

Hypergeometric2F1[-(37/8), -(11/8), 5/2, z] == (1/(58913925 z^(3/2))) (16 ((-Sqrt[z]) (41847 - 5152868 z - 22599262 z^2 - 11324556 z^3 + 793799 z^4 - 105800 z^5 + 8280 z^6) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) (4 (-13949 + 502164 z + 3647469 z^2 - 1394498 z^3 - 2927187 z^4 + 211416 z^5 - 27485 z^6 + 2070 z^7) Sin[(3 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]