Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8378)

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=7/3, b>=a

For fixed z and a=7/3, b=17/3

http://functions.wolfram.com/07.23.03.8378.01

Input Form

Hypergeometric2F1[7/3, 17/3, -(9/2), -z] == ((107495424 + 1665515520 z + 12767330304 z^2 + 67394371584 z^3 + 308979810304 z^4 + 2150891077632 z^5 - 7651283181855 z^6 + 2950602965636 z^7 + 30303976416 z^8 + 2410036416 z^9 + 119014144 z^10) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-35831808 - 529956864 z - 3885596672 z^2 - 19769851904 z^3 - 89360646144 z^4 + 2416130220893 z^5 - 1641298613956 z^6 + 29143588512 z^7 + 2350529344 z^8 + 119014144 z^9) Sinh[ArcSinh[Sqrt[z]]/3])/(107495424 (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]