Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4m6)

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=-43/8

http://functions.wolfram.com/07.23.03.b4m6.01

Input Form

Hypergeometric2F1[-(47/8), -(43/8), 9/4, z] == (1/(12485873295 z^2)) (2 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (2 (-4322919 + 817031691 z + 19375132977 z^2 + 92183545723 z^3 + 136239684963 z^4 + 68386508505 z^5 + 10649163475 z^6 + 347828385 z^7) + (1/Sqrt[1 - z]) (8645838 - 1638386301 z - 34812846669 z^2 - 121954758913 z^3 - 45700929973 z^4 + 121552527593 z^5 + 73768982985 z^6 + 8666723925 z^7 + 110041515 z^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]