Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4653)

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=-4/3

http://functions.wolfram.com/07.23.03.4653.01

Input Form

Hypergeometric2F1[-(17/3), -(4/3), 9/2, z] == (243 (Sqrt[z] (884736 - 15990784 z + 169017344 z^2 + 10603415383 z^3 + 2701506269 z^4 - 12933962644 z^5 - 605892128 z^6 + 91266944 z^7 - 10928128 z^8 + 683008 z^9) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (-2654208 + 47185920 z - 493420544 z^2 + 6671171584 z^3 + 41491688733 z^4 + 27201796996 z^5 - 564143264 z^6 + 86059008 z^7 - 10586624 z^8 + 683008 z^9) Sin[ArcSin[Sqrt[z]]/3]))/ (3128350390165 Sqrt[1 - z] z^(7/2))

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]