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

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=31/8

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

Input Form

Hypergeometric2F1[-(31/8), 31/8, 9/2, z] == (1/(243376947 z^(7/2))) (256 (Sqrt[z] (2480 + 3131 z + 8618 z^2 + 1020459 z^3 - 3694240 z^4 + 5049440 z^5 - 3103232 z^6 + 722304 z^7) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) (8 (-1240 - 713 z - 3131 z^2 - 31744 z^3 + 300267 z^4 - 734525 z^5 + 813846 z^6 - 433048 z^7 + 90288 z^8) Sin[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]