Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View
Applied and Computational Mathematics
Volume 3, Issue 2, April 2014, Pages: 57-62
Received: Mar. 27, 2014; Accepted: Apr. 24, 2014; Published: May 10, 2014
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Authors
Ramesh Naidu Annavarapu, Department of Physics, Pondicherry University, Puducherry – 605014, India
Vipin Srivastava, School of Physics, University of Hyderabad, Hyderabad – 500 046, India
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Abstract
The zeros and asymptotic limits of two new classes of orthogonal polynomials, which are derived by applying two orthogonalization procedures due to Löwdin to a set of monomials, are calculated. It is established that they possess all the properties ofthe zeros of a polynomial. Their asymptotic limits are found. A Unified view of all the Löwdin orthogonal polynomials together with the standard classical orthogonal polynomials are presented in a unique graph.
Keywords
Asymptotic Limits, Canonical Orthogonalization, Complex Zeros, Hermitian Metric Matrix, Positive-Definiteness, Symmetric Orthogonalization
To cite this article
Ramesh Naidu Annavarapu, Vipin Srivastava, Zeros and Asymptotic Limits of Löwdin Orthogonal Polynomials with a Unified View, Applied and Computational Mathematics. Vol. 3, No. 2, 2014, pp. 57-62. doi: 10.11648/j.acm.20140302.13
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