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

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.aawv.01

Input Form

Hypergeometric2F1[-(17/4), 5, 23/4, z] == (1/(412316860416 z^(19/4))) (209 (2 z^(3/4) (-1276275 - 1312740 z - 2068560 z^2 - 5237700 z^3 + 956729634 z^4 - 3197199180 z^5 + 4162358200 z^6 - 2462978700 z^7 + 555179625 z^8) + 69615 (-1 + z)^5 (55 + 308 z + 1050 z^2 + 2900 z^3 + 7975 z^4) ArcTan[z^(1/4)] - 69615 (-1 + z)^5 (55 + 308 z + 1050 z^2 + 2900 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]