Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aci1)

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=-13/4, b>=a

For fixed z and a=-13/4, b=5/4

http://functions.wolfram.com/07.23.03.aci1.01

Input Form

Hypergeometric2F1[-(13/4), 5/4, 6, z] == -((1/(25649298675 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((79872 - 602784 z + 1945125 z^2 - 3414840 z^3 + 3153150 z^4 - 5267724 z^5 + 3117653 z^6 - 974820 z^7 + 129360 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-79872 + 79872 Sqrt[z] + 542880 z - 542880 z^(3/2) - 1547325 z^2 + 1547325 z^(5/2) + 2314455 z^3 - 2314455 z^(7/2) - 1576575 z^4 + 1576575 z^(9/2) + 1168629 z^5 - 1168629 z^(11/2) - 428120 z^6 + 428120 z^(13/2) + 64680 z^7 - 64680 z^(15/2)) 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]