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Series Expansions for Dual Laguerre Temperatures

Published online by Cambridge University Press:  20 November 2018

Deborah Tepper Haimo
Deborah Tepper Haimo*
Affiliation:
University of Missouri, St. Louis, Missouri
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In a recent paper [2], the author, with F. M. Cholewinski, derived criteria for the series expansions of solutions u(x, t) of the Laguerre differential heat equation xuxx + (α + 1 - x)ux = ut in terms of the Laguerre heat polynomials and of their temperature transforms. Our present goal is the characterization of those solutions which are representable in a Maclaurin double series in xe-t and in 1 — e-t Some of the results are analogous to those derived by D. V. Widder in [4] for the classical heat equation and by the author in [1] for the generalized heat equation.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1145 - 1153
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Haimo, D. T., Series representations of generalized temperature functions, SIAM J. Appl. Math. 15 (1967), 359–367.Google Scholar
2. Haimo, D. T. and Cholewinski, F. M., The dual Poisson Laguerre transform, Trans. Amer. Math. Soc. 14 (1969), 271–300.Google Scholar
3. Haimo, D. T. and Cholewinski, F. M., Expansions in terms of Laguerre heat polynomials and of their temperature transforms, J. Analyse Math. 24 (1971), 285–322.Google Scholar
4. Widder, D. V., Analytic solutions of the heat equation, Duke Math. J. 29 (1962), 497–504.Google Scholar