Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb9k)

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=-27/8

http://functions.wolfram.com/07.23.03.bb9k.01

Input Form

Hypergeometric2F1[-(37/8), -(27/8), 9/2, z] == (1/(584513104175 z^(7/2))) (256 ((-Sqrt[z]) (154512 - 3441111 z + 47924472 z^2 - 3238758269 z^3 - 16868078610 z^4 - 19566481233 z^5 - 5959906916 z^6 - 332864763 z^7 + 2211726 z^8) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) (2 (-103008 + 2382060 z - 33905727 z^2 + 664218117 z^3 + 4994171853 z^4 + 2433269257 z^5 - 5295027725 z^6 - 2599125377 z^7 - 166985313 z^8 + 1105863 z^9) 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]