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Logarithmic solutions of Bianchi's equation

Bateman, H. (1933) Logarithmic solutions of Bianchi's equation. Proceedings of the National Academy of Sciences of the United States of America, 19 (9). pp. 852-854. ISSN 0027-8424. http://resolver.caltech.edu/CaltechAUTHORS:BATpnas33

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Abstract

The partial differential equation ∂^nV/∂x1∂x2…∂xn = MV was discussed by Bianchi(1) with the aid of the methods of Riemann and Picard. The results were extended to a more general equation which was also studied by Niccoletti.(2) The original equation, for a constant value of M, was studied later by Sibirani(3) in connection with a generalization of the Bessel function and some partial differential equations were listed which could be solved with the aid of this function. The case in which M is constant has also been studied by Chaundy(4) who gives some solutions in the form of definite integrals which we wish to obtain here with the aid of Murphy's theorem.


Item Type:Article
Additional Information:© 1933 by the National Academy of Sciences. Communicated July 20, 1933.
Record Number:CaltechAUTHORS:BATpnas33
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BATpnas33
Alternative URL:http://www.pnas.org/cgi/reprint/19/9/852
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9329
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Dec 2007
Last Modified:26 Dec 2012 09:47

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