Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb6s)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-37/8, b>=a

For fixed z and a=-37/8, b=-35/8

http://functions.wolfram.com/07.23.03.bb6s.01

Input Form

Hypergeometric2F1[-(37/8), -(35/8), 7/2, z] == (1/(8992509295 z^(5/2))) (64 (Sqrt[z] (38628 - 1258629 z + 185809498 z^2 + 1532131549 z^3 + 2935164480 z^4 + 1654025125 z^5 + 248451490 z^6 + 5529315 z^7) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((-51504 + 1722165 z - 61833771 z^2 - 855531159 z^3 - 1329930151 z^4 + 789226015 z^5 + 1218270175 z^6 + 232598915 z^7 + 5529315 z^8) Sin[(3 ArcSin[Sqrt[z]])/4])))

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]