Results 11 to 20 of about 78,037 (158)
On conjectures of Stenger in the theory of orthogonal polynomials
Journal of Inequalities and Applications, 2019 The conjectures in the title deal with the zeros xj $x_{j}$, j=1,2,…,n $j=1,2, \ldots ,n$, of an orthogonal polynomial of degree n>1 $n>1$ relative to a nonnegative weight function w on an interval [a,b] $[a,b]$ and with the respective elementary ...
Walter Gautschi, Ernst Hairer
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Symmetry, Integrability and Geometry: Methods and Applications, 2013 We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing.
Ernest G. Kalnins +2 more
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Chained-Function Filter Synthesis Based on the Modified Jacobi Polynomials [PDF]
Radioengineering, 2018 A new class of filter functions with pass-band ripple which derives its origin from a method of determining the chained function lowpass filters described by Guglielmi and Connor is introduced.
G. Perenic +3 more
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Operational Approach and Solutions of Hyperbolic Heat Conduction Equations
Axioms, 2016 We studied physical problems related to heat transport and the corresponding differential equations, which describe a wider range of physical processes. The operational method was employed to construct particular solutions for them.
Konstantin Zhukovsky
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Shape invariant hypergeometric type operators with application to quantum mechanics
, 2006 A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators.
A.F. Nikiforov +6 more
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Orthogonality of Hermite polynomials in superspace and Mehler type formulae [PDF]
, 2011 In this paper, Hermite polynomials related to quantum systems with orthogonal O(m)-symmetry, finite reflection group symmetry G < O(m), symplectic symmetry Sp(2n) and superspace symmetry O(m) x Sp(2n) are considered.
Coulembier, Kevin +2 more
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Eigenvalue Integro-Differential Equations for Orthogonal Polynomials on the Real Line
, 1994 The one-dimensional harmonic oscillator wave functions are solutions to a Sturm-Liouville problem posed on the whole real line. This problem generates the Hermite polynomials.
Askey R. +3 more
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Digital Repository of Mathematical Formulae
, 2014 The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF addresses needs of
Cohl, Howard S. +4 more
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Pseudo-factorials, elliptic functions, and continued fractions
, 2009 This study presents miscellaneous properties of pseudo-factorials, which are numbers whose recurrence relation is a twisted form of that of usual factorials.
Bacher, Roland, Flajolet, Philippe
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Some Orthogonal Polynomials Arising from Coherent States [PDF]
, 2011 We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature.
Akhiezer N I +19 more
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