Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6412)

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=-8/3, b>=a

For fixed z and a=-8/3, b=17/3

http://functions.wolfram.com/07.23.03.6412.01

Input Form

Hypergeometric2F1[-(8/3), 17/3, -(11/2), z] == (1/(12124728 (-1 + z)^8)) ((1/Sqrt[1 - z]) ((12124728 - 70421400 z + 148103424 z^2 - 111971680 z^3 - 10474992 z^4 - 14262864 z^5 - 69492192 z^6 + 272241927 z^7 - 359867560 z^8 + 240691984 z^9 - 83039424 z^10 + 11824384 z^11) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (4041576 - 20629728 z + 35161056 z^2 - 14014528 z^3 - 11330704 z^4 - 12901504 z^5 + 159851051 z^6 - 266966232 z^7 + 203606416 z^8 - 77127232 z^9 + 11824384 z^10) 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]