Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8797)

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=13/3, b>=a

For fixed z and a=13/3, b=17/3

http://functions.wolfram.com/07.23.03.8797.01

Input Form

Hypergeometric2F1[13/3, 17/3, -(9/2), z] == ((1/Sqrt[1 - z]) ((6019743744 - 120469192704 z + 1238900539392 z^2 - 9235841024000 z^3 + 64377562726400 z^4 - 765096897675264 z^5 - 5497483479296033 z^6 - 6657666627510916 z^7 - 2140351098600504 z^8 - 149259271118432 z^9 + 148232116352 z^10) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (2006581248 - 38744358912 z + 385856438272 z^2 - 2809986285568 z^3 + 19510028009472 z^4 + 1288763591981155 z^5 + 2511290669912660 z^6 + 1126734651961512 z^7 + 107161350074464 z^8 + 148232116352 z^9) Sin[ArcSin[Sqrt[z]]/3])/(6019743744 (-1 + z)^14)

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]