Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.al9j)

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=9/4, b>=a

For fixed z and a=9/4, b=4

http://functions.wolfram.com/07.23.03.al9j.01

Input Form

Hypergeometric2F1[9/4, 4, -(21/4), z] == (1/(238 (-1 + z)^12)) (2 (119 - 1632 z + 10692 z^2 - 45344 z^3 + 145930 z^4 - 431648 z^5 + 2813124 z^6 - 646046 z^7 - 1760495 z^8 - 87010 z^9 + 2310 z^10) - 231 Sqrt[1 - z] z^(25/4) (-11803 - 6105 z - 185 z^2 + 5 z^3) 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]