Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7187)

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=-2/3, b>=a

For fixed z and a=-2/3, b=14/3

http://functions.wolfram.com/07.23.03.7187.01

Input Form

Hypergeometric2F1[-(2/3), 14/3, -(11/2), z] == (1/(13856832 (-1 + z)^9)) ((1/Sqrt[1 - z]) ((-13856832 + 124571520 z - 489989952 z^2 + 1089942272 z^3 - 1451105920 z^4 + 1021427968 z^5 + 239479680 z^6 - 278225043 z^7 + 145570082 z^8 - 40185416 z^9 + 4717024 z^10) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (-4618944 + 38273472 z - 136751616 z^2 + 269848832 z^3 - 302988928 z^4 + 143687808 z^5 - 219035463 z^6 + 127246258 z^7 - 37826904 z^8 + 4717024 z^9) 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]