Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aada)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-17/4, b>=a

For fixed z and a=-17/4, b=-7/4

http://functions.wolfram.com/07.23.03.aada.01

Input Form

Hypergeometric2F1[-(17/4), -(7/4), 6, z] == (1/(177738647261175 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((452608 - 6980064 z + 54578823 z^2 - 310815726 z^3 + 1823636529 z^4 + 29661403464 z^5 + 25382632473 z^6 + 2542047354 z^7 - 94789233 z^8 + 3634092 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-452608 + 452608 Sqrt[z] + 6640608 z - 6640608 z^(3/2) - 49651407 z^2 + 49651407 z^(5/2) + 274335477 z^3 - 274335477 z^(7/2) - 1623421800 z^4 + 1623421800 z^(9/2) - 9152247654 z^5 + 9152247654 z^(11/2) - 4175240751 z^6 + 4175240751 z^(13/2) - 45728991 z^7 + 45728991 z^(15/2) + 1817046 z^8 - 1817046 z^(17/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

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]