Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bfh2)

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=-31/8, b>=a

For fixed z and a=-31/8, b=29/8

http://functions.wolfram.com/07.23.03.bfh2.01

Input Form

Hypergeometric2F1[-(31/8), 29/8, -(7/2), -z] == (1/(116480 (1 + z)^(25/8))) ((116480 - 107120 z + 174759 z^2 - 445237 z^3 + 2910544 z^4 + 15808896 z^5 + 19126272 z^6 + 7028736 z^7) Cos[ArcTan[Sqrt[z]]/4] - Sqrt[z] (-29120 + 35880 z - 57291 z^2 + 133393 z^3 + 2773728 z^4 + 4232448 z^5 + 1757184 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]