Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8590)

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=10/3, b>=a

For fixed z and a=10/3, b=14/3

http://functions.wolfram.com/07.23.03.8590.01

Input Form

Hypergeometric2F1[10/3, 14/3, -(11/2), z] == ((1/Sqrt[1 - z]) ((-1773674496 + 29059596288 z - 232639782912 z^2 + 1240388141056 z^3 - 5198286168064 z^4 + 20667863580672 z^5 - 135747203981312 z^6 - 512568830157907 z^7 - 276594034170054 z^8 - 27029315566184 z^9 + 37058029088 z^10) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (-591224832 + 9270484992 z - 71068336128 z^2 + 364141690880 z^3 - 1481640517632 z^4 + 5872171819008 z^5 + 154969821129977 z^6 + 133334699896362 z^7 + 18765375079560 z^8 + 37058029088 z^9) Sin[ArcSin[Sqrt[z]]/3])/(1773674496 (-1 + z)^13)

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]