Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T21:24:07.730Z Has data issue: false hasContentIssue false

Some Continued Fractions of Ramanujan and Meixner-Pollaczek Polynomials

Published online by Cambridge University Press:  20 November 2018

David R. Masson*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada, M5S 1A1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We examine the convergence and analytic properties of a continued fraction of Ramanujan and its connection to the orthogonal polynomials of Meixner-Pollaczek.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Akhiezer, N. I., The Classical Moment Problem (Oliver and Boyd, Edinburgh and London, 1965).Google Scholar
2. Askey, R. and Wimp, J., Associated Laguerre and Hermite polynomials, Proc. Roy. Soc. Edinburgh, 96A (1984), pp. 1537.Google Scholar
3. Berndt, B. C., Lamphere, R. L. and Wilson, B. M., Chapter 12 of Ramanujaris second notebook; continued fractions, Rocky Mtn. J. Math. 15 (1985), pp. 235-310.Google Scholar
4. Erd, A.élyi, Ed., Higher Transcendental Functions, Vol. 1 (McGraw-Hill, New York, 1953).Google Scholar
5. Gautschi, W., Computational aspects of three-term recurrence relations, SIAM Review 9 (1967), pp. 24-82.Google Scholar
6. Jones, W. B. and Thron, W. J., Continued Fractions Analytic Theory and Applications, (Addison- Wesley, Reading, 1980).Google Scholar
7. Masson, D., Difference equations, continued fractions, Jacobi matrices and orthogonal polynomials Nonlinear Numerical Methods and Rational Approximation, Cuyt, A., éd., (D. Reidel, Dordrecht, 1988), pp. 239257.Google Scholar
8. Masson, D., Convergence and analytic continuation for a class of regular C-fractions, Canad. Math. Bull. 28(1985), pp. 411421.Google Scholar
9. Pincherle, S., Délie funzioni ipergeometriche e di varie questioni ad esse attinenti, Gion. Mat. Battaglini, 32 (1894), pp. 209-291.Google Scholar
10. Ramanujan, S., Notebooks, Vol. 2 (Tata Institute of Fundamental Research, Bombay, 1957).Google Scholar
11. Wall, H. S., Analytic Theory of Continued Fractions (Von Nostrand, Princeton, 1948).Google Scholar