Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5950)

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=17/3

http://functions.wolfram.com/07.23.03.5950.01

Input Form

Hypergeometric2F1[-(11/3), 17/3, -(11/2), z] == (1/(551124 (-1 + z)^7)) ((1/Sqrt[1 - z]) ((-551124 + 2082024 z - 2035152 z^2 - 205376 z^3 - 233528 z^4 - 526064 z^5 - 3564848 z^6 + 18625399 z^7 - 30542408 z^8 + 24356176 z^9 - 9753536 z^10 + 1580800 z^11) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (-183708 + 564732 z - 295092 z^2 - 239604 z^3 - 252252 z^4 - 372204 z^5 + 9872031 z^6 - 21527896 z^7 + 20072208 z^8 - 8963136 z^9 + 1580800 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]