Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8884)

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=16/3, b>=a

For fixed z and a=16/3, b=17/3

http://functions.wolfram.com/07.23.03.8884.01

Input Form

Hypergeometric2F1[16/3, 17/3, -(9/2), z] == ((1/Sqrt[1 - z]) (9 (-1337720832 + 29793189888 z - 345398837248 z^2 + 2950822887424 z^3 - 24090095124480 z^4 + 345650738757632 z^5 + 3105066034019791 z^6 + 5033640090386424 z^7 + 2446719685787144 z^8 + 348588711736480 z^9 + 9735726955392 z^10) Cos[ArcSin[Sqrt[z]]/3]) - Sqrt[z] (4013162496 - 86555492352 z + 975595372544 z^2 - 8172437504000 z^3 + 66591109939200 z^4 + 5954381514835157 z^5 + 15457728217165216 z^6 + 10336180741932216 z^7 + 1926101963833376 z^8 + 70130152868992 z^9) Sin[ArcSin[Sqrt[z]]/3])/(12039487488 (-1 + z)^15)

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]