Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9xu)

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.a9xu.01

Input Form

Hypergeometric2F1[-(19/4), 6, 15/4, z] == (1/(545259520 z^(11/4))) (4 z^(3/4) (10241 + 144837 z + 138973493 z^2 - 1136554407 z^3 + 3410127315 z^4 - 4822339137 z^5 + 3263919351 z^6 - 854314461 z^7) + 4389 (1 - z)^(5/2) (-7 - 115 z - 2070 z^2 + 64170 z^3 - 224595 z^4 + 194649 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]