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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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.
|Additional Information:||© 1933 by the National Academy of Sciences. Communicated July 20, 1933.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||13 Dec 2007|
|Last Modified:||26 Dec 2012 09:47|
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