Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b53c)

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=-47/8, b>=a

For fixed z and a=-47/8, b=5/8

http://functions.wolfram.com/07.23.03.b53c.01

Input Form

Hypergeometric2F1[-(47/8), 5/8, 3/2, -z] == (1/(4125033 Sqrt[z] (1 + z)^(1/8))) (4 (Sqrt[z] (1140169 + 2770867 z + 4521723 z^2 + 4546481 z^3 + 2761056 z^4 + 933120 z^5 + 135168 z^6) Cos[ArcTan[Sqrt[z]]/4] - (435643 + 477333 z + 873461 z^2 + 958631 z^3 + 623436 z^4 + 222720 z^5 + 33792 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]