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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.

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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.

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Additional Information:© 1933 by the National Academy of Sciences. Communicated July 20, 1933.
Issue or Number:9
Record Number:CaltechAUTHORS:BATpnas33
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9329
Deposited By: Tony Diaz
Deposited On:13 Dec 2007
Last Modified:02 Oct 2019 23:59

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