Search results for "Orthogonal polynomials"
showing 10 items of 21 documents
Products of Bessel functions and associated polynomials
2013
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
Indefinite integrals for some orthogonal polynomials obtained using integrating factors
2020
A method has been presented recently for deriving integrals of special functions using two kinds of integrating factor for the homogeneous second-order linear differential equations which many spec...
Error analysis of the orthogonal series solution of linear time-invariant systems
1989
Similarities in the error analysis of the polynomial series solution of linear time-invariant systems are pointed out.
On an Inequality for Legendre Polynomials
2020
This paper is concerned with the orthogonal polynomials. Upper and lower bounds of Legendre polynomials are obtained. Furthermore, entropies associated with discrete probability distributions is a topic considered in this paper. Bounds of the entropies which improve some previously known results are obtained in terms of inequalities. In order to illustrate the results obtained in this paper and to compare them with other results from the literature some graphs are provided.
The Vector QD Algorithm for Smooth Functions (f, f′)
1996
AbstractWe deal with the functionz↦(f(z), f′(z)) wheref(z)=∑i⩾0aizi, (ai∈C) with limi→∞ai+1×ai−1/(ai)2=q. We investigate the convergence of the vector QD algorithm. We give the asymptotic behaviour of the generalized Hankel determinants. A convergence result on the vector orthogonal polynomials is proved.
Indefinite integrals of special functions from inhomogeneous differential equations
2018
A method is presented for deriving integrals of special functions which obey inhomogeneous second-order linear differential equations. Inhomogeneous equations are readily derived for functions sati...
Relative differential forms and complex polynomials
2000
A Rayleigh-Ritz approach for postbuckling analysis of variable angle tow composite stiffened panels
2018
Abstract A Rayleigh-Ritz solution approach for generally restrained multilayered variable angle tow stiffened plates in postbuckling regime is presented. The plate model is based on the first order shear deformation theory and accounts for geometrical nonlinearity through the von Karman’s assumptions. Stiffened plates are modelled as assembly of plate-like elements and penalty techniques are used to join the elements in the assembled structure and to apply the kinematical boundary conditions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed to build the trial functions. A computer code was developed to implement the propose…
On Pietsch measures for summing operators and dominated polynomials
2012
We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\mu)$, where $\mu$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $\mu$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials.
Convergence and applications of vector rational approximations
1992
The Padé approximants and their generalizations are for many years the matter of intense researchs .Yet , many theoritical problems stay in suspense : problems of exitence and unicity , problems of convergence and acceleration of convergence .The purpose of the present work vas to give answers to such questions .In the first section we take an in terest in vector Padé approximants of matrix series .Conditions of existence and unicity ,results of convergence are given ,as also the link with the theory of Lanczos method for the resolution of linear Systems . We utilize also the vector Padé approximants to provide a simultaneous approximation of a function and its derivative .In the second sec…