Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aai1)

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=1/4

http://functions.wolfram.com/07.23.03.aai1.01

Input Form

Hypergeometric2F1[-(17/4), 1/4, 5, z] == (1/(128246493375 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] ((-84864 + 859248 z - 4206735 z^2 + 15169440 z^3 + 60579750 z^4 - 18399612 z^5 + 5953409 z^6 - 1279740 z^7 + 129360 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 4 (-21216 + 21216 Sqrt[z] + 198900 z - 198900 z^(3/2) - 904995 z^2 + 904995 z^(5/2) + 3135990 z^3 - 3135990 z^(7/2) + 1744050 z^4 - 1744050 z^(9/2) - 611688 z^5 + 611688 z^(11/2) + 145145 z^6 - 145145 z^(13/2) - 16170 z^7 + 16170 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]