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. https://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 | ||||||
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| Additional Information: | © 1934 by the National Academy of Sciences. Communicated December 12, 1933. | ||||||
| Issue or Number: | 1 | ||||||
| Record Number: | CaltechAUTHORS:BATpnas34 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:BATpnas34 | ||||||
| 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: | 02 Oct 2019 23:59 |
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