A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤a<b≤∞ then the sequence of (monic) polynomials {Qn}, defined by ∫a ...

A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤a<b≤∞ then the sequence of (monic) polynomials {Qn}, defined by ∫a ...

The principal objective here is to look at some algebraic properties of the orthogonal polynomials Ψn (b,s,t) n with respect to the Sobolev inner product on the unit circle <f,g>S (b,s,t) = (1 − t) <f,g>μ(b) + t f(1) g(1) ...

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained ...

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained ...

In this article we consider the Sobolev orthogonal polynomials associated to the Jacobi's measure on [-1, 1]. It is proven that for the class of monic Jacobi-Sobolev orthogonal polynomials, the smallest closed interval ...

We refer to a pair of non trivial probability measures (μ0, μ1) supported on the unit circle as a coherent pair of measures of the second kind on the unit circle if the corresponding sequences of monic orthogonal polynomials ...

A result of Pólya states that every sequence of quadrature formulas Q n (f) with n nodes and positive Cotes numbers converges to the integral I(f) of a continuous function f provided Q n (f) = I(f) for a space of algebraic ...