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Note on the Polynomials which satisfy the Differential Equation

Published online by Cambridge University Press:  20 January 2009

Neil M'Arthur
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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