Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5650)

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=-11/3, b>=a

For fixed z and a=-11/3, b=-10/3

http://functions.wolfram.com/07.23.03.5650.01

Input Form

Hypergeometric2F1[-(11/3), -(10/3), 9/2, -z] == (243 ((-Sqrt[z]) (4423680 + 88211456 z + 1068957696 z^2 - 98880840411 z^3 + 119577643045 z^4 + 124656989376 z^5 - 88031374080 z^6 + 6755289920 z^7) Cosh[ArcSinh[Sqrt[z]]/3] + 9 Sqrt[1 + z] (1474560 + 28966912 z + 347930624 z^2 + 5784862720 z^3 - 50050618433 z^4 + 64791255656 z^5 - 19297505120 z^6 + 982004160 z^7) Sinh[ArcSinh[Sqrt[z]]/3]))/ (28317665220065 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]