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There are a number of equations known as the Riccati differential equation. The most common is z^2w^('')+[z^2-n(n+1)]w=0 (1) (Abramowitz and Stegun 1972, p. 445; Zwillinger ...

A formula is called satisfiable if it takes at least one true value in some interpretation.

The Schur polynomials are a class of orthogonal polynomials. They are a special case of the Jack polynomials corresponding to the case alpha=1.

The series of Sturm functions arising in application of the Sturm theorem.

Solving the wave equation on a disk gives a solution in terms of Bessel functions.

A surface represented parametrically by elliptic functions.

Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) (1) is the multinomial coefficient ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from ...