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Homogeneous solutions of the generalized heat equation

Published online by Cambridge University Press:  09 April 2009

E. Kochneff
Affiliation:
Department of Mathematics Eastern Washington UniversityCheney WA 99004USA e-mail: ekochneff@ewu.edu
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Abstract

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We discuss expansions of solutions of the generalized heat equation which have a singularity at zero in terms of two sequences of homogeneous solutions.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Bragg, L. R., ‘Radial heat polynomials and related functions’, Trans. Amer. Math. Soc. 119 (1965), 270290.CrossRefGoogle Scholar
[2]Erdelyi, A., Quart. J. Math. Oxford Ser. (2) 9 (1938), 196198.Google Scholar
[3]Hadamard, J., Lectures on Cauchy's problem in linear partial differential equations (Dover, New York, 1952).Google Scholar
[4]Haimo, D. T., ‘Expansions in terms of generalized heat polynomials and of their Appell transforms’, J. Appl. Math. Mech. 15 (1966), 735758.Google Scholar
[5], ‘Homogeneous generalized temperatures’, SIAM J. Math. Anal. 11 (1980), 473478.CrossRefGoogle Scholar
[6]Kochneff, E. and Sagher, Y., ‘The Appell transform and the semigroup property for temperatures’, J. Austral. Math. Soc. (Series A) 60 (1996), 109117.CrossRefGoogle Scholar
[7]Krall, A. and Morton, R., ‘Distributional weight functions for orthogonal polynomials’, SIAM J. Math. Anal. 9 (1978), 604626.Google Scholar
[8]Lebedev, N. N., Special functions and their applications (Prentice-Hall, New Jersey, 1965).CrossRefGoogle Scholar
[9]Rosenbloom, P. C. and Widder, D. V., [Expansions in terms of heat polynomials and associated functions’, Trans. Amer. Math. Soc. 92 (1959), 604626.CrossRefGoogle Scholar
[10]Szego, G., Orthogonal polynomials, Amer. Math. Soc. Colloq. Pub. 23 (Amer. Math. Soc., Providence, 1979).Google Scholar