Orthogonal polynomials for Minkowski’s question mark function

A generating function for Laguerre-Sobolev orthogonal polynomials

Let fSng denote the sequence of polynomials orthogonal with respect to the Sobolev inner product

The Minkowski question mark function: explicit series for the dyadic period function and moments

Previously, several natural integral transforms of the Minkowski question mark function F (x) were introduced by the author. Each of them is uniquely characterized by certain regularity conditions and the functional equation, thus encoding intrinsic information about F (x). One of them, the dyadic period function G(z), was defined as a Stieltjes transform. In this paper we introduce a family of...

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.