- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 873078, 10 pages
Approximate Closed-Form Formulas for the Zeros of the Bessel Polynomials
Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana, 58060 Morelia, MN, Mexico
Received 11 June 2012; Revised 10 September 2012; Accepted 23 September 2012
Academic Editor: Stefan Samko
Copyright © 2012 Rafael G. Campos and Marisol L. Calderón. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- H. L. Krall and O. Frink, “A new class of orthogonal polynomials: the Bessel polynomials,” Transactions of the American Mathematical Society, vol. 65, pp. 100–115, 1949.
- E. Grosswald, Bessel Polynomials, vol. 698 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1978.
- H. M. Srivastava, “Some orthogonal polynomials representing the energy spectral functions for a family of isotropic turbulence fields,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 64, no. 6, pp. 255–257, 1984.
- J. L. López and N. M. Temme, “Large degree asymptotics of generalized Bessel polynomials,” Journal of Mathematical Analysis and Applications, vol. 377, no. 1, pp. 30–42, 2011.
- Ö. Eğecioğlu, “Bessel polynomials and the partial sums of the exponential series,” SIAM Journal on Discrete Mathematics, vol. 24, no. 4, pp. 1753–1762, 2010.
- C. Berg and C. Vignat, “Linearization coefficients of Bessel polynomials and properties of Student -distributions,” Constructive Approximation, vol. 27, no. 1, pp. 15–32, 2008.
- L. Pasquini, “Accurate computation of the zeros of the generalized Bessel polynomials,” Numerische Mathematik, vol. 86, no. 3, pp. 507–538, 2000.
- A. J. Carpenter, “Asymptotics for the zeros of the generalized Bessel polynomials,” Numerische Mathematik, vol. 62, no. 4, pp. 465–482, 1992.
- F. W. J. Olver, “The asymptotic expansion of Bessel functions of large order,” Philosophical Transactions of the Royal Society of London Series A, vol. 247, pp. 328–368, 1954.
- H.-J. Runckel, “Zero-free parabolic regions for polynomials with complex coefficients,” Proceedings of the American Mathematical Society, vol. 88, no. 2, pp. 299–304, 1983.
- M. G. de Bruin, E. B. Saff, and R. S. Varga, “On the zeros of generalized Besselpolynomials I, II,” Indagationes Mathematicae, vol. 84, pp. 1–25, 1981.
- F. Gálvez and J. S. Dehesa, “Some open problems of generalised Bessel polynomials,” Journal of Physics A, vol. 17, no. 14, pp. 2759–2766, 1984.
- E. Hendriksen and H. van Rossum, “Electrostatic interpretation of zeros,” in Orthogonal Polynomials and Their Applications, M. Alfaro, J. S. Dehesa, F. J. Marcellan, J. L. Rubio de Francia, and J. Vinuesa, Eds., vol. 1329 of Lecture Notes in Mathematics, pp. 241–250, Springer, Berlin, Germany, 1988.
- G. Valent and W. Van Assche, “The impact of Stieltjes' work on continued fractions and orthogonal polynomials: additional material,” Journal of Computational and Applied Mathematics, vol. 65, no. 1–3, pp. 419–447, 1995.
- G. Szegő, Orthogonal Polynomials, Colloquium Publications, American Mathematical Society, Providence, RI, USA, 1975.
- F. Marcellán, A. Martínez-Finkelshtein, and P. Martinez-Gonzalez, “Electrostatic models for zeros of polynomials: old, new, and some open problems,” Journal of Computational and Applied Mathematics, vol. 207, pp. 258–272, 2007.
- R. G. Campos, “Perturbed zeros of classical orthogonal polynomials,” Boletin de la Sociedad Matematica Mexicana, vol. 5, no. 1, pp. 143–153, 1999.
- R. G. Campos, “Solving singular nonlinear two-point boundary value problems,” Boletin de la Sociedad Matematica Mexicana, vol. 3, no. 2, pp. 279–297, 1997.
- R. G. Campos and L. A. Avila, “Some properties of orthogonal polynomials satisfying fourth order differential equations,” Glasgow Mathematical Journal, vol. 37, no. 1, pp. 105–113, 1995.