Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4795)

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=8/3

http://functions.wolfram.com/07.23.03.4795.01

Input Form

Hypergeometric2F1[-(17/3), 8/3, 9/2, z] == (1/(2131900225 z^(7/2))) (243 ((1/Sqrt[1 - z]) (Sqrt[z] (117504 - 400384 z - 52224 z^2 + 7961595 z^3 - 27906591 z^4 + 45963732 z^5 - 43521712 z^6 + 24414208 z^7 - 7587840 z^8 + 1011712 z^9) Cos[ArcSin[Sqrt[z]]/3]) + (-352512 + 1096704 z + 435200 z^2 + 2680832 z^3 - 15441751 z^4 + 31263644 z^5 - 33843888 z^6 + 20999680 z^7 - 7081984 z^8 + 1011712 z^9) Sin[ArcSin[Sqrt[z]]/3]))

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]