Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5j1)

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=-47/8, b>=a

For fixed z and a=-47/8, b=31/8

http://functions.wolfram.com/07.23.03.b5j1.01

Input Form

Hypergeometric2F1[-(47/8), 31/8, 9/2, -z] == (256 (Sqrt[z] Sqrt[1 + z] (-303056 + 473525 z - 1723631 z^2 + 337881797 z^3 + 1823533547 z^4 + 4141751746 z^5 + 5080923760 z^6 + 3542840928 z^7 + 1328557824 z^8 + 208986624 z^9) Cosh[ArcSinh[Sqrt[z]]/4] - 2 (-606112 + 530348 z - 2746445 z^2 + 36328838 z^3 + 471568504 z^4 + 1717269598 z^5 + 3157114917 z^6 + 3349668080 z^7 + 2090498256 z^8 + 716525568 z^9 + 104493312 z^10) Sinh[ArcSinh[Sqrt[z]]/4]))/(81531277245 z^(7/2) Sqrt[1 + z])

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]