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Some Continued Fractions of Ramanujan and Meixner-Pollaczek Polynomials

Published online by Cambridge University Press:  20 November 2018

David R. Masson
David R. Masson*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada, M5S 1A1
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Abstract

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

Keywords

30B7040A1539A1033A6533A1533A30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 2 , 01 June 1989 , pp. 177 - 181
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. 15–37.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. 239–257.Google Scholar
8. Masson, D., Convergence and analytic continuation for a class of regular C-fractions, Canad. Math. Bull. 28(1985), pp. 411–421.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