Skip to main content
×
×
Home

On q-Exponential Functions for |q| = 1

  • D. S. Lubinsky (a1)
Abstract

We discuss the q-exponential functions eq, Eq for q on the unit circle, especially their continuity in q, and analogues of the limit relation

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      On q-Exponential Functions for |q| = 1
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      On q-Exponential Functions for |q| = 1
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      On q-Exponential Functions for |q| = 1
      Available formats
      ×
Copyright
References
Hide All
1. Askey, R., The q-gamma and q-beta functions. Appl. Anal. 8 (1978), 125141.
2. Askey, R., Ramanujan's Extensions of the Gamma and Beta Functions. Amer. Math. Monthly 87 (1980), 346359.
3. Driver, K. A., Convergence of Padé Approximants for Some q-hypergeometric Series (Wynn's Power Series I,II and III). Ph. D Thesis, Witwatersrand University, Johannesburg, 1991.
4. Driver, K. A. and Lubinsky, D. S., Convergence of Padé Approximants for a q-hypergeometric Series (Wynn's Power Series I). Aequationes Math. 42 (1991), 85106.
5. Driver, K. A. and Lubinsky, D. S., Convergence of Padé Approximants for a q-hypergeometric Series (Wynn's Power Series II). Colloq. Math. (Janos Bolyai Society) 58 (1990), 221239.
6. Driver, K. A. and Lubinsky, D. S., Convergence of Padé Approximants for a q-hypergeometric Series (Wynn's Power Series III). Aequationes Math. 45 (1993), 123.
7. Driver, K. A., Lubinsky, D. S., Petruska, G. and Sarnak, P., Irregular Distribution of fnågÒ n = 1Ò2Ò3Ò ð ð ð. Quadrature of Singular Integrands and Curious Basic Hypergeometric Series, Indag. Math. 2 (1991), 469481.
8. Exton, R., q-Hypergeometric Functions and Applications. Ellis Horwood, Chichester, 1983.
9. Fine, N. J., Basic Hypergeometric Series and Applications. Math. Surveys and Monographs 27, Amer. Math. Soc., Providence, 1988.
10. Gasper, G. and Rahman, M., Basic Hypergeometric Series. Cambridge University Press, Cambridge, 1990.
11. Hardy, G. H. and Littlewood, J. E., Note on the Theory of Series (XXIV): A curious Power Series. Proc. Cambridge Philos. Soc. 42 (1946), 8590.
12. Hardy, G. H. and Wright, E. M., An Introduction to the Theory of Numbers. Oxford University Press, Oxford, 1975, Fourth Edition with corrections.
13. Hille, E. M., Analytic Function Theory. Vol. 2, Chelsea, New York, 1987.
14. Lubinsky, D. S., Note on Polynomial Approximation of Monomials and Diophantine Approximation. J. Approx. Theory 43 (1985), 2935.
15. Lubinsky, D. S. and Saff, E. B., Convergence of Padé Approximants of Partial Theta Functions and the Rogers-Szegö Polynomials. Constr. Approx. 3 (1987), 331361.
16. McIntosh, R. J., Some Asymptotic Formulae for Ramanujan's Mock-Theta Functions. In: Contemporary Mathematics 166, (eds. G. Andrews et al), Amer. Math Soc., Providence, 1994, 189–196.
17. Pastro, P. I., Orthogonal Polynomials and Some q-beta integrals of Ramanujan. J. Math. Anal. Appl. 112 (1985), 517540.
18. Petruska, G., On the Radius of Convergence of q-Series. Indag. Math. 3 (1992), 353364.
19. Spiridonov, V. and Zhedanov, A., Discrete Darboux Transformations, Discrete time Toda lattice and the Askey-Wilson polynomials. Methods Appl. of Anal. 2 (1995), 369398.
20. Spiridonov, V. and Zhedanov, A., Zeros and Orthogonality of the Askey-Wilson Polynomials for q a Root of Unity. manuscript.
21. Zhedanov, A., On the Polynomials Orthogonal on Regular Polygons. manuscript.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed