Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7951)

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=4/3, b>=a

For fixed z and a=4/3, b=11/3

http://functions.wolfram.com/07.23.03.7951.01

Input Form

Hypergeometric2F1[4/3, 11/3, -(11/2), -z] == (1/(5038848 (1 + z)^(21/2))) ((5038848 + 57666816 z + 306858240 z^2 + 1017979648 z^3 + 2419546624 z^4 + 4739727872 z^5 + 11995206144 z^6 - 11300723435 z^7 - 135750508 z^8 - 7438384 z^9) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (1679616 + 18040320 z + 89720064 z^2 + 277513216 z^3 + 617484800 z^4 + 1163736064 z^5 - 5819564225 z^6 + 132031316 z^7 + 7438384 z^8) Sinh[ArcSinh[Sqrt[z]]/3])

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]