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The iterated equation of generalized axially symmetric potential theory. III. Conjugate general solutions

Published online by Cambridge University Press:  09 April 2009

J. C. Burns
J. C. Burns
Affiliation:
The Australian National University Canberra, A.C.T.
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The iterated equation of generalized axially symmetric potential theory (GASPT), in the notation of the first paper of this series [1] which will be designated I, is the equation where the operator Lk is defined by

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 3 , August 1967 , pp. 290 - 300
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Burns, J. C., ‘The iterated equation of generalized axially symmetric potential theory. I Particular solutions’, Journ. Austr. Math. Soc., 7 (1967), 263–276.CrossRefGoogle Scholar
[2]Beltrami, E., Opere Matematiche, vol. 3 (1911), 349–382.Google Scholar
[3]Courant, R. and Hilbert, D., Methods of Mathematical Physics, vol 2 (Interscience, 1962): supplement to chapter 4, especially p. 389.Google Scholar
[4]Parsons, D. H., ‘Irrotational flow of a liquid with axial symmetry’, Proc. Edin. Math. Soc. (2) 13 (1963), 201–204.CrossRefGoogle Scholar