Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5837)

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=-11/3, b>=a

For fixed z and a=-11/3, b=8/3

http://functions.wolfram.com/07.23.03.5837.01

Input Form

Hypergeometric2F1[-(11/3), 8/3, 11/2, z] == (1/(426380045 z^(9/2))) (6561 ((1/Sqrt[1 - z]) (Sqrt[z] (-2592 + 12000 z - 16800 z^2 + 352 z^3 + 57997 z^4 - 114569 z^5 + 97100 z^6 - 40144 z^7 + 6656 z^8) Cos[ArcSin[Sqrt[z]]/3]) + (7776 - 33696 z + 41440 z^2 + 7392 z^3 + 26400 z^4 - 78993 z^5 + 79524 z^6 - 36816 z^7 + 6656 z^8) 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]