# regular singular point

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## regular singular point

[′reg·yə·lər ¦siŋ·gyə·lər ′pȯint]
(mathematics)
A regular singular point of a differential equation is a singular point of the equation at which none of the solutions has an essential singularity.
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Solution of equation (14) for the oscillating part of the velocity is obtained as a power series, using regular singular point method, in the form [17]
We consider the general Sturm-Liouville problem on (a,[infinity]), assuming that the left endpoint x = a is either (1) regular, or (2) nonoscillatory for all real [Lambda] and a regular singular point.
Currently SLEDGE is only capable of handling the special case when x = a is a regular singular point of (1.
In general, when x = a is not a regular singular point but satisfies the requirement of being nonoscillatory for all real [Lambda], a normalization of the principal solution [Phi] which can be easily implemented numerically is not known.
2) When x = a is a singular endpoint, the assumption that it is also a regular singular point is needed to implement the normalization (1.
Among specific topics are the complex exponential function, two basic equations and their monodromy, regular singular points and the local Riemann-Hilbert correspondence, the universal group as the pro-algebraic hull of the fundamental group, and beyond local fuschian differential Galois theory.
to solve algebraic systems, the Laplace transform and the series method for solution about ordinary and regular singular points (Froebenius method [1-3]).

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