Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4823)

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=11/3

http://functions.wolfram.com/07.23.03.4823.01

Input Form

Hypergeometric2F1[-(17/3), 11/3, -(11/2), -z] == (1/19683) ((1/(1 + z)^(7/2)) ((19683 - 4374 z + 5130 z^2 - 7952 z^3 + 15963 z^4 - 46722 z^5 + 341120 z^6 + 1588704 z^7 + 1802112 z^8 + 632320 z^9) Cosh[ArcSinh[Sqrt[z]]/3]) + (1/(1 + z)^3) (Sqrt[z] (-6561 + 6075 z - 6489 z^2 + 7929 z^3 - 11778 z^4 + 24960 z^5 + 924768 z^6 + 1485952 z^7 + 632320 z^8) Sinh[ArcSinh[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]