Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8891)

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=16/3, b>=a

For fixed z and a=16/3, b=17/3

http://functions.wolfram.com/07.23.03.8891.01

Input Form

Hypergeometric2F1[16/3, 17/3, -(3/2), -z] == (1/(7077888 (1 + z)^(25/2))) ((7077888 + 231473152 z + 8325169152 z^2 - 146893458567 z^3 + 413676503840 z^4 - 319986586632 z^5 + 68028439200 z^6 - 2696508800 z^7) Cosh[ArcSinh[Sqrt[z]]/3] + 9 Sqrt[z] Sqrt[1 + z] (-262144 - 8388608 z + 2685584429 z^2 - 13271556376 z^3 + 14980932472 z^4 - 4352983840 z^5 + 233493120 z^6) 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]