Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8630)

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=17/3

http://functions.wolfram.com/07.23.03.8630.01

Input Form

Hypergeometric2F1[10/3, 17/3, -(9/2), z] == ((1/Sqrt[1 - z]) ((-1504935936 + 26717257728 z - 239781445632 z^2 + 1526605152256 z^3 - 8819619364864 z^4 + 83097823936512 z^5 + 446915012924593 z^6 + 357290677228928 z^7 + 55794764834736 z^8 - 198575099264 z^9 + 5593664768 z^10) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (-501645312 + 8552742912 z - 73947086848 z^2 + 457469788160 z^3 - 2623322161152 z^4 - 118479191490067 z^5 - 155043365243848 z^6 - 35854748353008 z^7 - 195778266880 z^8 + 5593664768 z^9) Sin[ArcSin[Sqrt[z]]/3])/(1504935936 (-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]