Ultrasmall Double Junction in Terms of Orthogonal Polynomials

Roots of Polynomials Expressed in Terms of Orthogonal Polynomials

A technique is presented for determining the roots of a polynomial p(x) that is expressed in terms of an expansion in orthogonal polynomials. The roots are expressed as the eigenvalues of a nonstandard companion matrix Bn whose coefficients depend on the recurrence formula for the orthogonal polynomials, and on the coefficients of the orthogonal expansion. Some questions on the numerical stabil...

Orthogonal Polynomials

The theory of orthogonal polynomials plays an important role in many branches of mathematics, such as approximation theory (best approximation, interpolation, quadrature), special functions, continued fractions, differential and integral equations. The notion of orthogonality originated from the theory of continued fractions, but later became an independent (and possibly more important) discipl...

Orthogonal Polynomials

Orthogonal Polynomials

In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.

Orthogonal Polynomials with Orthogonal Derivatives