Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8376)

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=7/3, b>=a

For fixed z and a=7/3, b=17/3

http://functions.wolfram.com/07.23.03.8376.01

Input Form

Hypergeometric2F1[7/3, 17/3, -(11/2), -z] == ((3547348992 + 56614256640 z + 438562308096 z^2 + 2240994836480 z^3 + 8869967183872 z^4 + 32516107796480 z^5 + 188396584026112 z^6 - 578222647391221 z^7 + 195897391111180 z^8 + 1736133702368 z^9 + 124459041088 z^10 + 5593664768 z^11) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-1182449664 - 18039324672 z - 133583929344 z^2 - 654336294912 z^3 - 2505811247104 z^4 - 9121021476864 z^5 + 191460450769887 z^6 - 111626034548876 z^7 + 1676001806112 z^8 + 121662208704 z^9 + 5593664768 z^10) Sinh[ArcSinh[Sqrt[z]]/3])/ (3547348992 (1 + z)^(27/2))

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]