Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4577)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-17/3, b>=a

For fixed z and a=-17/3, b=-13/3

http://functions.wolfram.com/07.23.03.4577.01

Input Form

Hypergeometric2F1[-(17/3), -(13/3), 5/2, z] == -((27 (Sqrt[z] (-524288 - 534724627 z - 4071829407 z^2 - 4122607790 z^3 + 4287885392 z^4 + 3945575760 z^5 + 495371200 z^6 + 853760 z^7) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (1572864 - 131596288 z - 4105333425 z^2 - 18954823374 z^3 - 23840335408 z^4 - 8700900720 z^5 - 703688640 z^6 + 853760 z^7) Sin[ArcSin[Sqrt[z]]/3]))/ (15626125825 Sqrt[1 - z] z^(3/2)))

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]