Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9o3)

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=-35/8

http://functions.wolfram.com/07.23.03.b9o3.01

Input Form

Hypergeometric2F1[-(39/8), -(35/8), 5/2, -z] == -((1/(34357 z^(3/2) (1 + z)^(1/8))) (16 (Sqrt[z] (-1 - 2222 z + 20097 z^2 - 40260 z^3 + 22385 z^4 - 3054 z^5 + 47 z^6) Cos[ArcTan[Sqrt[z]]/4] + 4 (1 + 75 z - 2090 z^2 + 8382 z^3 - 8811 z^4 + 2519 z^5 - 140 z^6) Sin[ArcTan[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]