Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4916)

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=17/3

http://functions.wolfram.com/07.23.03.4916.01

Input Form

Hypergeometric2F1[-(17/3), 17/3, -(11/2), z] == (1/(216513 (-1 + z)^5)) ((1/Sqrt[1 - z]) ((-216513 - 61236 z - 88587 z^2 - 173890 z^3 - 458415 z^4 - 1848704 z^5 - 19855693 z^6 + 157231308 z^7 - 359224944 z^8 + 379708160 z^9 - 194438400 z^10 + 39203840 z^11) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (-72171 - 71199 z - 85176 z^2 - 126070 z^3 - 252395 z^4 - 809523 z^5 + 69967196 z^6 - 230034064 z^7 + 297190400 z^8 - 174836480 z^9 + 39203840 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]