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Functions orthogonal in the Hermitian sense. A new application of basic numbers

Bateman, H. (1934) Functions orthogonal in the Hermitian sense. A new application of basic numbers. Proceedings of the National Academy of Sciences of the United States of America, 20 (1). pp. 63-66. ISSN 0027-8424. http://resolver.caltech.edu/CaltechAUTHORS:BATpnas34

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Abstract

To find a particular set of functions Hn(u) satisfying the Hermitian relation Im,n ≡ ∫∞ -∞ e^-1/2x^2 Hm(ix)Hn(-ix)dx = 0 in which the exponential factor is exp (-x2/2) as also in (14) we may put z = e^iax, where a is an arbitrary positive constant and assume that Hn(ix) is a polynomial of the nth degree in z with real coefficients.


Item Type:Article
Additional Information:© 1934 by the National Academy of Sciences. Communicated December 12, 1933.
Issue or Number:1
Record Number:CaltechAUTHORS:BATpnas34
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BATpnas34
Alternative URL:http://www.pnas.org/cgi/reprint/20/1/63
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9379
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Dec 2007
Last Modified:14 Nov 2014 19:20

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