NDLI: Real Zeros of a Random Sum of Orthogonal Polynomials

Content Provider	Scilit
Author	Das, Minaketan
Copyright Year	1971
Description	Let be a sequence of normally distributed independent random variables with mathematical expectation zero and variance unity. Let be the normalised Legendre polynomials orthogonal with respect to the interval . It is proved that the average number of the zeros of in the same interval is asymptotically equal to when is large.
Related Links	http://www.ams.org/proc/1971-027-01/S0002-9939-1971-0268933-9/S0002-9939-1971-0268933-9.pdf
Ending Page	153
Page Count	7
Starting Page	147
ISSN	00029939
e-ISSN	10886826
DOI	10.2307/2037279
Journal	Proceedings of the American Mathematical Society
Issue Number	1
Volume Number	27
Language	English
Publisher	Duke University Press
Access Restriction	Open
Subject Keyword	Logic Mathematical Physics Real Zeros Orthogonal Polynomials Random Sum Sum of Orthogonal
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Real Zeros of a Random Sum of Orthogonal Polynomials