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

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=13/4

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

Input Form

Hypergeometric2F1[-(17/4), 13/4, 5, z] == (4096 (4 (7072 + 7072 Sqrt[z] - 13260 z - 13260 z^(3/2) - 8619 z^2 - 8619 z^(5/2) - 19448 z^3 - 19448 z^(7/2) + 450285 z^4 + 450285 z^(9/2) - 1047354 z^5 - 1047354 z^(11/2) + 1051820 z^6 + 1051820 z^(13/2) - 506352 z^7 - 506352 z^(15/2) + 96096 z^8 + 96096 z^(17/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (28288 - 60112 z - 23205 z^2 - 66521 z^3 + 1011065 z^4 - 2233011 z^5 + 2180024 z^6 - 1028720 z^7 + 192192 z^8) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(1665538875 Pi Sqrt[1 + Sqrt[z]] z^4)

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]