Results 41 to 50 of about 535,269 (286)
Dispersion Estimates for the Discrete Laguerre Operator [PDF]
, 2016 We derive an explicit expression for the kernel of the evolution group $\exp(-\mathrm{i} t H_0)$ of the discrete Laguerre operator $H_0$ (i.e. the Jacobi operator associated with the Laguerre polynomials) in terms of Jacobi polynomials.
Kostenko, Aleksey, Teschl, Gerald
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Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials
Mathematics, 2019 The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method.
H. Singh, R. Pandey, H. Srivastava
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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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Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space
International Journal of Mathematics and Mathematical Sciences, 2004 A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions.
Fred Brackx +2 more
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On the Behaviour of Zeros of Jacobi Polynomials
Journal of Approximation Theory, 2002 Denoting by \(x_{n,k}(\alpha,\beta)\) and \(x_{n,k}(\lambda)= x_{n,k} (\lambda-1/2, \lambda-1/2)\) the zeros, in decreasing order, of the Jacobi polynomial \(P_n^{(\alpha,\beta)} (x)\) and of the ultraspherical (or Gegenbauer) polynomial \(C_n^\lambda(x)\), respectively, the authors investigate the monotonicity of \(x_{n,k}(\alpha,\beta)\) as functions
Dimitrov, D. K., Rodrigues, R. O.
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, 1999 We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with point masses ...
Koekoek, J., Koekoek, R.
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A conjecture on Exceptional Orthogonal Polynomials [PDF]
, 2012 Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials.
A. González-López +42 more
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Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III [PDF]
, 2016 In a previous paper, we presented conjectures of the recurrence relations with constant coefficients for the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types.
Odake, Satoru
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Journal of Mathematical Analysis and Applications, 1994 The paper is devoted to eigenfunction expansions associated with Jacobi polynomials \([^{\alpha,\beta} P_ n]^ \infty_{n=0}\). The classical expansion associated with the Jacobi operator is well-known when \(a>-1\), \(\beta> -1\). It is shown that when \(\alpha\), \(\beta-1\).
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Generating functions for the Jacobi polynomial [PDF]
Proceedings of the American Mathematical Society, 1976 Two theorems are proved with the aid of operator and series iteration methods. Special cases appear to give new and known generating functions for the Jacobi polynomial.
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