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

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=6

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

Input Form

Hypergeometric2F1[-(17/4), 6, -(5/4), z] == -((1/(2621440 (-1 + z)^3)) (2621440 + 45613056 z + 2280652800 z^2 - 25120407550 z^3 + 85553050800 z^4 - 129784172700 z^5 + 91671259680 z^6 - 24649975350 z^7 - 10094175 (-1 + z)^3 z^(9/4) (221 - 1122 z + 1221 z^2) ArcTan[z^(1/4)] + 10094175 (-1 + z)^3 z^(9/4) (221 - 1122 z + 1221 z^2) 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]