Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8883)

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/07.23.03.8883.01

Input Form

Hypergeometric2F1[16/3, 17/3, -(11/2), -z] == ((397303087104 + 8760733728768 z + 97547593973760 z^2 + 753802447683584 z^3 + 4828645584535552 z^4 + 31522040818171904 z^5 + 376591230800232448 z^6 - 2913324988175000995 z^7 + 4140860613388633984 z^8 - 1791890564718868648 z^9 + 230107238666363680 z^10 - 5853151964371840 z^11) Cosh[ArcSinh[Sqrt[z]]/3] + 3 Sqrt[z] Sqrt[1 + z] (-44144787456 - 942350008320 z - 10178877456384 z^2 - 76663652089856 z^3 - 483315380387840 z^4 - 3167867734327296 z^5 + 218862099981444515 z^6 - 489262033319514184 z^7 + 287637470130599304 z^8 - 47833254490162400 z^9 + 1572070543984000 z^10) Sinh[ArcSinh[Sqrt[z]]/3])/(397303087104 (1 + z)^(33/2))

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]