Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6e2)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-17/8

http://functions.wolfram.com/07.23.03.b6e2.01

Input Form

Hypergeometric2F1[-(45/8), -(17/8), 19/4, z] == (1/(1623407386665 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1982904 + 39838344 z - 465715263 z^2 + 5912369490 z^3 + 158220400959 z^4 + 297875610612 z^5 + 103089628303 z^6 - 144298366 z^7 + 11226185 z^8 - 536176 z^9 - (1/Sqrt[1 - z]) (4 (-495726 + 10207449 z - 121346643 z^2 + 1535092815 z^3 + 13464264129 z^4 + 1779453009 z^5 - 14129185937 z^6 - 2678902851 z^7 + 151972385 z^8 - 11594806 z^9 + 536176 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]