Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4680)

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=-17/3, b>=a

For fixed z and a=-17/3, b=-1/3

http://functions.wolfram.com/07.23.03.4680.01

Input Form

Hypergeometric2F1[-(17/3), -(1/3), 11/2, -z] == -((6561 (Sqrt[z] (2322432 + 33423360 z + 240312320 z^2 + 1254735872 z^3 - 20958390497 z^4 - 19498739015 z^5 + 3217254490 z^6 + 885231728 z^7 + 201369968 z^8 + 30436544 z^9 + 2219776 z^10) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (-6967296 - 98205696 z - 692756480 z^2 - 3571335168 z^3 - 23406817280 z^4 + 56196638795 z^5 + 2841247914 z^6 + 795266768 z^7 + 186984112 z^8 + 29326656 z^9 + 2219776 z^10) Sinh[ArcSinh[Sqrt[z]]/3]))/(190829373800065 z^(9/2) 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]