Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5qr)

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=45/8

http://functions.wolfram.com/07.23.03.b5qr.01

Input Form

Hypergeometric2F1[-(47/8), 45/8, -(19/4), z] == (1/(50233568 2^(3/4) (-1 + z)^4)) ((1 + Sqrt[1 - z])^(3/4) (25116784 + 78985676 z + 220350207 z^2 + 679189686 z^3 + 2749402623 z^4 - 715465227312 z^5 + 2824893172992 z^6 - 4223450136576 z^7 + 2814450794496 z^8 - 704136609792 z^9 + (1/Sqrt[1 - z]) (25116784 + 66427284 z + 177717771 z^2 + 557571574 z^3 + 2376346275 z^4 + 757288921752 z^5 - 4038774898752 z^6 + 8467774267392 z^7 - 8805237129216 z^8 + 4554534420480 z^9 - 938848813056 z^10)))

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]