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A characterization of orthogonal polynomials

โœ Scribed by H.L Krall; I.M Sheffer

Publisher
Elsevier Science
Year
1964
Tongue
English
Weight
513 KB
Volume
8
Category
Article
ISSN
0022-247X

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๐Ÿ“œ SIMILAR VOLUMES

New Characterizations of Discrete Classi
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โœ K.H. Kwon; D.W. Lee; S.B. Park ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 358 KB

We prove that if both [P n (x)] n=0 and [{ r P n (x)] n=r are orthogonal polynomials for any fixed integer r 1, then [P n (x)] n=0 must be discrete classical orthogonal polynomials. This result is a discrete version of the classical Hahn's theorem stating that if both [P n (x)] n=0 and [(dร‚dx) r P n

Orthogonal Homogeneous Polynomials
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โœ A. Fryant; A. Naftalevich; M.K. Vemuri ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 71 KB

An addition formula, Pythagorean identity, and generating function are obtained for orthogonal homogeneous polynomials of several real variables. Application is made to the study of series of such polynomials. Results include an analog of the Funk-Hecke theorem.