Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8339)

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=14/3

http://functions.wolfram.com/07.23.03.8339.01

Input Form

Hypergeometric2F1[7/3, 14/3, -(9/2), -z] == ((26873856 + 375570432 z + 2566103040 z^2 + 11892801536 z^3 + 46934519808 z^4 + 273635180544 z^5 - 793845121997 z^6 + 236486700660 z^7 + 1495115184 z^8 + 59507072 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-8957952 - 118886400 z - 772395008 z^2 - 3429527552 z^3 - 13286563840 z^4 + 270379084647 z^5 - 139452981380 z^6 + 1465361648 z^7 + 59507072 z^8) Sinh[ArcSinh[Sqrt[z]]/3])/(26873856 (1 + z)^(23/2))

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]