Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4603)

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=-10/3

http://functions.wolfram.com/07.23.03.4603.01

Input Form

Hypergeometric2F1[-(17/3), -(10/3), 7/2, z] == (81 (Sqrt[z] (-2359296 + 75759616 z + 21955863881 z^2 + 78986429895 z^3 - 1106046296 z^4 - 78499996120 z^5 - 21293113440 z^6 - 119953280 z^7 + 3415040 z^8) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (7077888 - 225181696 z + 7798784000 z^2 + 130472124867 z^3 + 337857210344 z^4 + 224625245000 z^5 + 33224836320 z^6 - 118245760 z^7 + 3415040 z^8) Sin[ArcSin[Sqrt[z]]/3]))/(1990768430105 Sqrt[1 - z] z^(5/2))

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]