Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7vx)

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=-23/4, b>=a

For fixed z and a=-23/4, b=6

http://functions.wolfram.com/07.23.03.a7vx.01

Input Form

Hypergeometric2F1[-(23/4), 6, 19/4, z] == (1/(422685179904 z^(15/4))) (4 z^(3/4) (2590973 + 20694135 z + 163534140 z^2 + 107959421732 z^3 - 843851300034 z^4 + 2625514683498 z^5 - 4226082833700 z^6 + 3740770770660 z^7 - 1735112670291 z^8 + 330619696407 z^9) - 100947 (1 - z)^(9/2) (77 + 945 z + 8370 z^2 + 97650 z^3 - 1904175 z^4 + 3275181 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]