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Asymptotic analysis of generalized Hermite polynomials
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Diego Dominici
Veröffentlicht/Copyright:
25. September 2009
We analyze the polynomials Hnr(x) considered by Gould and Hopper, which generalize the classical Hermite polynomials. We present the main properties of Hnr(x) and derive asymptotic approximations for large values of n from their differential-difference equation, using a discrete ray method. We give numerical examples showing the accuracy of our formulas.
Keywords: Hermite polynomials; asymptotic analysis; ray method; differential-difference equations; discrete WKB method
Received: 2007-January-01
Revised: 2007-October-24
Published Online: 2009-09-25
Published in Print: 2008-02
© Oldenbourg Wissenschaftsverlag
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Artikel in diesem Heft
- The Dirichlet problem for graphs of prescribed anisotropic mean curvature in ℝn+1
- On the value distribution of two differential monomials
- The completely indeterminate Caratheodory matrix problem in the Rq[a, b] class
- Sum of the periodic zeta-function over the nontrivial zeros of the Riemann zeta-function
- On representations of Stokes flows and of the solutions of Navier's equation for linear elasticity
- Asymptotic analysis of generalized Hermite polynomials
- Some convergence theorems for Lebesgue integrals
- The zeros of certain differential polynomials
Schlagwörter für diesen Artikel
Hermite polynomials;
asymptotic analysis;
ray method;
differential-difference equations;
discrete WKB method
Artikel in diesem Heft
- The Dirichlet problem for graphs of prescribed anisotropic mean curvature in ℝn+1
- On the value distribution of two differential monomials
- The completely indeterminate Caratheodory matrix problem in the Rq[a, b] class
- Sum of the periodic zeta-function over the nontrivial zeros of the Riemann zeta-function
- On representations of Stokes flows and of the solutions of Navier's equation for linear elasticity
- Asymptotic analysis of generalized Hermite polynomials
- Some convergence theorems for Lebesgue integrals
- The zeros of certain differential polynomials
