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

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=45/8

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

Input Form

Hypergeometric2F1[-(37/8), 45/8, -(11/2), z] == (1/(45056 (1 - z)^(13/2))) (Sqrt[1 - z] (45056 - 69888 z - 21728 z^2 - 20037 z^3 - 28161 z^4 - 67707 z^5 - 494819 z^6 + 4672212 z^7 - 10380880 z^8 + 10401280 z^9 - 5026560 z^10 + 957440 z^11) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (33792 - 57344 z - 11732 z^2 - 10071 z^3 - 15719 z^4 - 44009 z^5 - 2013225 z^6 + 8839252 z^7 - 15013040 z^8 + 12794880 z^9 - 5505280 z^10 + 957440 z^11) 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]