Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9xb)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-19/4, b>=a

For fixed z and a=-19/4, b=6

http://functions.wolfram.com/07.23.03.a9xb.01

Input Form

Hypergeometric2F1[-(19/4), 6, -(17/4), z] == (1/(21725184 (-1 + z)^6)) (4 (5431296 + 3833856 z + 10027008 z^2 + 34570240 z^3 + 193069056 z^4 + 4762927104 z^5 - 37309614505 z^6 + 102904437057 z^7 - 144413695314 z^8 + 111661716474 z^9 - 45541532421 z^10 + 7688830149 z^11) - 4389 Sqrt[1 - z] z^(21/4) (-2419615 + 11130229 z - 20725254 z^2 + 19469178 z^3 - 9208395 z^4 + 1751841 z^5) Beta[z, 3/4, 1/2])

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]