Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8763)

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=13/3, b>=a

For fixed z and a=13/3, b=14/3

http://functions.wolfram.com/07.23.03.8763.01

Input Form

Hypergeometric2F1[13/3, 14/3, -(7/2), -z] == ((39813120 + 729907200 z + 7167082496 z^2 + 57358221312 z^3 + 714439557120 z^4 - 4979797344899 z^5 + 5388156890688 z^6 - 1378888235520 z^7 + 61568726720 z^8) Cosh[ArcSinh[Sqrt[z]]/3] - 3 Sqrt[z] Sqrt[1 + z] (4423680 + 77987840 z + 741801984 z^2 + 5856952320 z^3 - 398013055619 z^4 + 708913355784 z^5 - 257797743840 z^6 + 15861521600 z^7) Sinh[ArcSinh[Sqrt[z]]/3])/ (39813120 (1 + z)^(25/2))

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]