Approximate Closed-Form Formulas for the Zeros of the Bessel Polynomials
Copyright policy )Approximate Closed-Form Formulas for the Zeros of the Bessel Polynomials
We find approximate expressionsx̃(k,n,a)andỹ(k,n,a)for the real and imaginary parts of thekth zerozk=xk+iykof the Bessel polynomialyn(x;a). To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex plane are limit points of the zeros of the normalized Bessel polynomials. Thus, these zeros are first computed numerically through an implementation of the electrostatic interpretation formulas and then, a fit to the real and imaginary parts as functions ofk,nandais obtained. It is shown that the resulting complex numberx̃(k,n,a)+iỹ(k,n,a)isO(1/n2)-convergent tozkfor fixedk.
normalized Bessel polynomial, Numerical Analysis, Applied Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Matrix Valued Polynomials, Computer science, Orthogonal Polynomials, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Convergence Analysis of Iterative Methods for Nonlinear Equations, Algorithm, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Modeling and Simulation, 33C47, 33F05, 33C10, 30C15, Physical Sciences, QA1-939, Bessel polynomial, FOS: Mathematics, Approximation, electrostatic interpretation formulas, Mathematical Physics, Mathematics, Anomalous Diffusion Modeling and Analysis
normalized Bessel polynomial, Numerical Analysis, Applied Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Matrix Valued Polynomials, Computer science, Orthogonal Polynomials, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Convergence Analysis of Iterative Methods for Nonlinear Equations, Algorithm, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Modeling and Simulation, 33C47, 33F05, 33C10, 30C15, Physical Sciences, QA1-939, Bessel polynomial, FOS: Mathematics, Approximation, electrostatic interpretation formulas, Mathematical Physics, Mathematics, Anomalous Diffusion Modeling and Analysis
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