DEtools[regularsp] - compute the regular singular points of a second order non-autonomous linear ODE
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Calling Sequence
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regularsp(des, ivar, dvar)
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Parameters
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des
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second order linear ordinary differential equation or its list form
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ivar
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indicates the independent variable when des is a list with the ODE coefficients
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dvar
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indicates the dependent variable, required only when des is an ODE and the dependent variable is not obvious
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Description
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Important: The regularsp command has been deprecated. Use the superseding command DEtools[singularities], which computes both the regular and irregular singular points, instead.
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The regularsp command determines the regular singular points of a given second order linear ordinary differential equation. The ODE could be given as a standard differential equation or as a list with the ODE coefficients (see DEtools[convertAlg]). Given a linear ODE of the form
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p(x) y''(x) + q(x) y'(x) + r(x) y(x) = 0, p(x) <> 0, p'(x) <> 0
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a point alpha is considered to be a regular singular point if
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1) alpha is a singular point,
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2) limit( (x-alpha)*q(x)/p(x), x=alpha ) = 0 and
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limit( (x-alpha)^2*r(x)/p(x), x=alpha ) = 0.
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The results are returned in a list. In the event that no regular singular points are found, an empty list is returned.
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Examples
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Important: The regularsp command has been deprecated. Use the superseding command DEtools[singularities], which computes both the regular and irregular singular points, instead.
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An ordinary differential equation (ODE)
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Warning, DEtools[regularsp] has been superseded by DEtools[singularities]
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The coefficient list form
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You can convert convert an ODE to the coefficient list form using DEtools[convertAlg] form
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