Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8633)

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=10/3, b>=a

For fixed z and a=10/3, b=17/3

http://functions.wolfram.com/07.23.03.8633.01

Input Form

Hypergeometric2F1[10/3, 17/3, -(7/2), -z] == ((55738368 + 1000636416 z + 9558753280 z^2 + 73670524928 z^3 + 868612276224 z^4 - 5570443416043 z^5 + 5180036650984 z^6 - 921623286960 z^7 - 3808452608 z^8 - 119014144 z^9) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (18579456 + 320471040 z + 2962161664 z^2 + 22496280576 z^3 - 1387760137665 z^4 + 2165003027024 z^5 - 581094067440 z^6 + 3748945536 z^7 + 119014144 z^8) Sinh[ArcSinh[Sqrt[z]]/3])/ (55738368 (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]