An Equivalence Theorem for Series of Orthogonal Polynomials.

Solving singular integral equations by using orthogonal polynomials

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

Recurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials

Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),] $$‎ ‎x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x)‎,$$ ‎we find the coefficients $b_{i,j}^{(p,q,ell‎ ,‎,r)}$ in the expansion‎ $$‎ ‎x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell‎ ‎}y^{r}f^{(p,q)}(x,y) =sumli...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Buckling and vibration analysis of angle -ply symmetric laminated composite plates with fully elastic boundaries

The main focus of this paper is on efficiency analysis of two kinds of approximating functions (characteristic orthogonal polynomials and characteristic beam functions) that have been applied in the Rayleigh-Ritz method to determine the non-dimensional buckling and frequency parameters of an angle ply symmetric laminated composite plate with fully elastic boundaries. It has been observed that o...

Convergence of Linear and Nonlinear Pade Approximants from Series of Orthogonal Polynomials

Analogues of the Nuttall-Pommerenke theorem and Wallin-type theorems for classical Pade approximants, are proved for linear and nonlinear Pade approximants formed from series of orthogonal polynomials, corresponding to a distribution da(x) with at most finitely many sign changes.

Expansions of Distributions in Term of Generalized Heat Polynomials and Their Appell Transforms

This paper is concerned with expansions of distributions in terms of the generalized heat polynomials and of their Appell transforms. Two different techniques are used to prove theorems concerning expansions of distributions. A theorem which provides an orthogonal series expansion of generalized functions is also established. It is shown that this theorem gives an inversion formula for a certai...