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.

Hermite polynomialsCylindrical harmonicsHermite polynomialsBessel processUmbral calculuApplied MathematicsFOS: Physical sciencesMathematical Physics (math-ph)Bessel functionsClassical orthogonal polynomialsAlgebraComputational Mathematicssymbols.namesakeHermite polynomialComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONBessel polynomialsStruve functionsymbolsJacobi polynomialsHermite polynomials;Umbral calculus;Bessel functionsBessel functions; Hermite polynomials; Umbral calculus; Applied Mathematics; Computational MathematicsUmbral calculusMathematical PhysicsBessel functionMathematicsApplied Mathematics and Computation
researchProduct

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...

Hermite polynomialsGegenbauer polynomialsDifferential equationApplied Mathematics010102 general mathematics010103 numerical & computational mathematics01 natural sciencesIntegrating factorVDP::Teknologi: 500Linear differential equationSpecial functionsOrthogonal polynomialsLaguerre polynomialsApplied mathematics0101 mathematicsAnalysisMathematicsIntegral Transforms and Special Functions
researchProduct

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.

Hermite polynomialsMathematical analysisLinear systemComputer Science ApplicationsTheoretical Computer ScienceOrthogonal seriesLTI system theoryControl and Systems EngineeringError analysisOrthogonal polynomialsApplied mathematicsPolynomial seriesLegendre polynomialsMathematicsInternational Journal of Systems Science
researchProduct

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.

Inequalitylcsh:MathematicsGeneral Mathematicsmedia_common.quotation_subject010102 general mathematicsGegenbauerlcsh:QA1-939Legendre01 natural sciencesChebyshev filterUpper and lower bounds010101 applied mathematicsChebyshevOrthogonal polynomialsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComputer Science (miscellaneous)Probability distributionOrder (group theory)Applied mathematics0101 mathematicsEngineering (miscellaneous)Legendre polynomialshypergeometric representationmedia_commonMathematicsMathematics
researchProduct

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.

Mathematics(all)Numerical AnalysisGeneral MathematicsApplied Mathematics010102 general mathematics010103 numerical & computational mathematics01 natural sciencesConvergence (routing)Orthogonal polynomials0101 mathematicsAlgorithmComputingMilieux_MISCELLANEOUS[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]AnalysisMathematicsJournal of Approximation Theory
researchProduct

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...

Mathematics::General MathematicsDifferential equationApplied Mathematics010102 general mathematicsMathematical analysis010103 numerical & computational mathematicsParabolic cylinder function01 natural sciencesLegendre functionsymbols.namesakeLinear differential equationSpecial functionsOrthogonal polynomialssymbols0101 mathematicsAnalysisBessel functionMathematicsIntegral Transforms and Special Functions
researchProduct

Relative differential forms and complex polynomials

2000

Pure mathematicsMathematics(all)Gegenbauer polynomialsGeneral MathematicsDiscrete orthogonal polynomialsMathematical analysisAskey–Wilson polynomialsClassical orthogonal polynomialssymbols.namesakeMacdonald polynomialsDifference polynomialssymbolsJacobi polynomialsKoornwinder polynomialsMathematicsBulletin des Sciences Mathématiques
researchProduct

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…

Rayleigh–Ritz methodEngineeringSource codemedia_common.quotation_subjectComposite numberStructure (category theory)02 engineering and technologyPhysics::Fluid Dynamics0203 mechanical engineeringGeneral Materials ScienceBoundary value problemSettore ING-IND/04 - Costruzioni E Strutture AerospazialiVariable angle tow composites Composite stiffened plates Postbuckling analysis Rayleigh-Ritz method First Order Shear DeformationLegendre polynomialsCivil and Structural Engineeringmedia_commonbusiness.industryMechanical EngineeringStructural engineering021001 nanoscience & nanotechnologyFinite element methodComputer Science Applications020303 mechanical engineering & transportsModeling and SimulationOrthogonal polynomials0210 nano-technologybusinessComputers & Structures
researchProduct

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.

Unit sphereDiscrete mathematics28C15 46G25 47B10 47L22Mathematics::Functional AnalysisPure mathematicsAlgebra and Number TheoryDiscrete orthogonal polynomialsBanach spaceMeasure (mathematics)Functional Analysis (math.FA)Mathematics - Functional AnalysisClassical orthogonal polynomialsFactorizationOrthogonal polynomialsFOS: MathematicsCanonical mapMathematicsLinear and Multilinear Algebra
researchProduct

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…

[ MATH ] Mathematics [math]Biorthogonal polynomialsAcceleration of convergenceEpsilon algorithme vectorielApproximants de Padé vectorielsBiorthogonalitéPadé type approximantsEpsilon algorithme topologique[MATH] Mathematics [math]Topological epsilon algorithmAccélération de la convergencePolynômes biorthogonauxVector Padé approximants[MATH]Mathematics [math]Vector epsilon algorithmApproximants de type Padé
researchProduct