Skip to main content Accessibility help
×
Home

Generating Functions for Ultraspherical Functions

  • B. Viswanathan (a1)

Extract

The ultraspherical function

1.1

for |1 — x| < 2 is a solution of the differential equation

1.2

This equation has two independent solutions; of the two, only Pn (λ)(x) is analytic at x = 1, aside for some special values of λ, which we shall not consider.

    • 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.

      Generating Functions for Ultraspherical Functions
      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.

      Generating Functions for Ultraspherical Functions
      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.

      Generating Functions for Ultraspherical Functions
      Available formats
      ×

Copyright

References

Hide All
1. Bloh, E. L., On an expansion of Bess el functions in a series ofLegendre functions (from Math. Revs., 16 (1955), 587).
2. Brafman, F., Generating functions of Jacobi and related polynomials, Proc. Amer. Math. Soc.,£ (1951), 942949.
3. Brafman, F., An ultraspherical generating function, Pacific J. Math., 7 (1957), 13191323.
4. Brafman, F., A generating function for associated Legendre polynomials, Quart. J. Math., 8 (1957), 8183.
5. Carlitz, L., Some generating functions for the Jacobi polynomials, Boll. Un. Math. Ital., 16 1961), 150155.
6. Rainville, E. D., Special functions (New York, 1960).
7. Szego, G., Orthogonal polynomials, Colloquium Publications 23 (Amer. Math. Soc, New York, 1959).
8. Toscano, L., Funzione generatice dei prodotti di polinomi diLaguerre con gli ultrasferici (from Math. Revs., (1951), 333).
9. Truesdell, C., A unified theory of special functions (Princeton, 1948).
10. Watson, G. N., Theory of Bessel functions (Cambridge, 1952).
11. Weisner, L., Group theoretic origin of certain generating functions, Pacific J. Math., 5 (1955), 10331039.
12. Weisner, L., Generating functions for Hermite functions, Can. J. Math., 11 (1959), 141147.
13. Weisner, L., Generating functions for Bessel functions, Can. J. Math., 11 (1959), 148155.
14. Yadao, G. M., Generating functions for associated Legendre polynomials, Quart. J. Math., 10 (1963), 120122.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

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