


What are regular singular points of a differential equation, and how might a discriminant-like term appear in their analysis?
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- Consider a linear homogeneous recurrence relation with constant coefficients; does a discriminant-like term appear in the analysis of its characteristic equation and solutions?
- How might the discriminant of a related polynomial or expression provide information about these singularities?
- How can these mistakes be avoided?
- Can the discriminant be used to analyze the behavior of solitons or other localized waves in nonlinear dispersive equations?
- How is the discriminant related to the study of special functions, like Bessel functions or hypergeometric functions?
- What is the height of a polynomial or an algebraic number?
- Are there any philosophical or historical debates surrounding the concept of the discriminant in mathematics?
- How is the discriminant related to the determinant of the matrix of the quadratic form?
- What is the geometric interpretation of the magnitude of the discriminant?
- What are the properties of quadratic forms over different types of rings?
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