Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-07T12:35:07.030Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on the Polynomials which satisfy the Differential Equation

Published online by Cambridge University Press:  20 January 2009

Neil M'Arthur
Rights & Permissions [Opens in a new window]

Extract

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.

Laguerre has shown that if be expanded in ascending powers of t,

where fn(x) is a polynomial of degree n, satisfying the differential equation

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , February 1919 , pp. 27 - 33
Copyright
Copyright © Edinburgh Mathematical Society 1919

References

* Laguerre, , Œuvres, T. I., p. 436Google Scholar. Abel, , Œuvres, T. II., p. 284. (1881).Google Scholar

* The result requires modification if p is a negative integer. In this case the second solution of (6) is required to express the coefficients for which n > −p.

* Loc. Cit., p. 428.

* Theorie des Integrallogarithmus, Leipzig (1906); p. 45