Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4628)

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=-7/3

http://functions.wolfram.com/07.23.03.4628.01

Input Form

Hypergeometric2F1[-(17/3), -(7/3), 7/2, -z] == -((81 (Sqrt[z] (589824 + 15728640 z - 3079273519 z^2 + 6494643579 z^3 + 4641090450 z^4 - 4866815576 z^5 + 87723840 z^6 + 6915456 z^7 + 341504 z^8) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (-1769472 - 46661632 z - 1281753088 z^2 + 16000395621 z^3 - 27267464342 z^4 + 8735970520 z^5 + 84394176 z^6 + 6744704 z^7 + 341504 z^8) Sinh[ArcSinh[Sqrt[z]]/3]))/(284395490015 z^(5/2) 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]