Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ad2o)

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=-5/4

http://functions.wolfram.com/07.23.03.ad2o.01

Input Form

Hypergeometric2F1[-(11/4), -(5/4), 6, z] == (1/(1400465491425 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((22528 - 268576 z + 1562385 z^2 - 6286665 z^3 + 24243450 z^4 + 208683774 z^5 + 73950117 z^6 + 82875 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-22528 + 22528 Sqrt[z] + 251680 z - 251680 z^(3/2) - 1376265 z^2 + 1376265 z^(5/2) + 5282970 z^3 - 5282970 z^(7/2) - 20431950 z^4 + 20431950 z^(9/2) - 52488504 z^5 + 52488504 z^(11/2) - 6878625 z^6 + 6878625 z^(13/2) + 165750 z^7 - 165750 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]