Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aa8n)

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=-15/4

http://functions.wolfram.com/07.23.03.aa8n.01

Input Form

Hypergeometric2F1[-(17/4), -(15/4), 5, z] == (1/(4512611027925 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] ((-28288 + 597584 z - 7265817 z^2 + 87034662 z^3 + 3452730825 z^4 + 8275360356 z^5 + 4729097097 z^6 + 632954694 z^7 + 9388071 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + 8 (3536 - 3536 Sqrt[z] - 72046 z + 72046 z^(3/2) + 854607 z^2 - 854607 z^(5/2) - 10246665 z^3 + 10246665 z^(7/2) - 163751370 z^4 + 163751370 z^(9/2) - 263257632 z^5 + 263257632 z^(11/2) - 94348773 z^6 + 94348773 z^(13/2) - 6052569 z^7 + 6052569 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]