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

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=-11/4, b>=a

For fixed z and a=-11/4, b=7/4

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

Input Form

Hypergeometric2F1[-(11/4), 7/4, 6, z] == (1/(16476064605 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((-157696 + 963424 z - 2343495 z^2 + 2630397 z^3 - 525525 z^4 + 673335 z^5 - 312000 z^6 + 54600 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (157696 - 157696 Sqrt[z] - 845152 z + 845152 z^(3/2) + 1728111 z^2 - 1728111 z^(5/2) - 1426425 z^3 + 1426425 z^(7/2) - 375375 z^4 + 375375 z^(9/2) + 948285 z^5 - 948285 z^(11/2) - 542100 z^6 + 542100 z^(13/2) + 109200 z^7 - 109200 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]