Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8887)

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/07.23.03.8887.01

Input Form

Hypergeometric2F1[16/3, 17/3, -(7/2), -z] == ((445906944 + 10340794368 z + 132552851456 z^2 + 1443536568320 z^3 + 25912505794560 z^4 - 277879136845673 z^5 + 524384058335344 z^6 - 290815983194808 z^7 + 46537374809696 z^8 - 1441278800512 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + 3 Sqrt[z] Sqrt[1 + z] (-49545216 - 1114112000 z - 13947895808 z^2 - 150661496832 z^3 + 18452755906409 z^4 - 57022660531912 z^5 + 44167822065624 z^6 - 9353985047456 z^7 + 381604855936 z^8) Sinh[ArcSinh[Sqrt[z]]/3])/ (445906944 (1 + z)^(29/2))

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]