Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5cx)

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=21/8

http://functions.wolfram.com/07.23.03.b5cx.01

Input Form

Hypergeometric2F1[-(47/8), 21/8, 11/2, -z] == (1024 (Sqrt[z] (15012928 + 80158312 z + 120338001 z^2 - 53483556 z^3 + 3820590286 z^4 + 11315879076 z^5 + 16022237609 z^6 + 13305189408 z^7 + 6652622592 z^8 + 1866805248 z^9 + 227082240 z^10) Cos[ArcTan[Sqrt[z]]/4] - (60051712 + 339399408 z + 576623777 z^2 - 87262644 z^3 + 502463934 z^4 + 2007911804 z^5 + 3212288681 z^6 + 2883366864 z^7 + 1527512448 z^8 + 448960512 z^9 + 56770560 z^10) Sin[ArcTan[Sqrt[z]]/4]))/(3759497784075 z^(9/2) (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]