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

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=-11/4, b>=a

For fixed z and a=-11/4, b=6

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

Input Form

Hypergeometric2F1[-(11/4), 6, 23/4, z] == -((1/(1635778560 z^(19/4))) (19 (4 z^(3/4) (-5929 - 16093 z - 43197 z^2 - 144529 z^3 - 22412875 z^4 + 74138361 z^5 - 79647183 z^6 + 28164213 z^7) - 231 (1 - z)^(5/2) (-77 - 385 z - 1330 z^2 - 4370 z^3 - 19665 z^4 + 121923 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]