Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8u2)

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=-21/4, b>=a

For fixed z and a=-21/4, b=17/4

http://functions.wolfram.com/07.23.03.a8u2.01

Input Form

Hypergeometric2F1[-(21/4), 17/4, 4, z] == -((1/(555179625 Pi z^3)) (256 Sqrt[1 + Sqrt[z]] ((3808 + 20349 z + 164220 z^2 - 10482175 z^3 + 50085750 z^4 - 99352176 z^5 + 99479072 z^6 - 49969920 z^7 + 10053120 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-3808 + 3808 Sqrt[z] - 23205 z + 23205 z^(3/2) - 182070 z^2 + 182070 z^(5/2) + 6005395 z^3 - 6005395 z^(7/2) - 21681000 z^4 + 21681000 z^(9/2) + 31234896 z^5 - 31234896 z^(11/2) - 20377280 z^6 + 20377280 z^(13/2) + 5026560 z^7 - 5026560 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]