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

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=21/8

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

Input Form

Hypergeometric2F1[-(31/8), 21/8, 9/2, -z] == (256 (Sqrt[z] (57040 + 134757 z - 64883 z^2 + 4298299 z^3 + 10384579 z^4 + 10437280 z^5 + 5005056 z^6 + 946176 z^7) Cos[ArcTan[Sqrt[z]]/4] - 2 (114080 + 305164 z - 54901 z^2 + 299460 z^3 + 988087 z^4 + 1130402 z^5 + 588672 z^6 + 118272 z^7) Sin[ArcTan[Sqrt[z]]/4]))/ (1054633437 z^(7/2) (1 + z)^(1/8))

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]