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

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=-17/4, b>=a

For fixed z and a=-17/4, b=5

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

Input Form

Hypergeometric2F1[-(17/4), 5, -(1/4), z] == (1/(524288 (-1 + z))) (-2 (262144 + 22020096 z - 296566445 z^2 + 1021677475 z^3 - 1302148575 z^4 + 555179625 z^5) - 69615 z^(5/4) (663 - 6188 z + 17850 z^2 - 20300 z^3 + 7975 z^4) ArcTan[z^(1/4)] + 69615 z^(5/4) (663 - 6188 z + 17850 z^2 - 20300 z^3 + 7975 z^4) ArcTanh[z^(1/4)])

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]