AUTHOR AND | 1LOKANATH SAHOO and 2MINAKETAN MAHANTI |
KEYWORDS: | Expected Number of Real zeros, Kac-Rice Formula, Normal Density, Jacobi Polynomial |
Issue Date: | August 2014 |
Pages: | |
ISSN: | 2319-8044 (Online) – 2231-346X (Print) |
Source: | Vol.26 – No.2 |
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DOI: | jusps-A |
ABSTRACT:
Let be a random polynomial such that ( ) is a sequence of mutually independent normally distributed random variables with mean zero and variance one; ( ) be a sequence of normalized Jacobi polynomials , orthogonal with respect to the interval (-1,1). It is proved that the average number of points of inflection of the random equation y=0 is asymptotic to .
Copy the following to cite this Article:
1LOKANATH SAHOO and 2MINAKETAN MAHANTI, “Average Number of Points of Inflection of a random sum of orthogonal polynomials”, Journal of Ultra Scientist of Physical Sciences, Volume 26, Issue 2, Page Number , 2016
Copy the following to cite this URL:
1LOKANATH SAHOO and 2MINAKETAN MAHANTI, “Average Number of Points of Inflection of a random sum of orthogonal polynomials”, Journal of Ultra Scientist of Physical Sciences, Volume 26, Issue 2, Page Number , 2016
Available from: http://www.ultrascientist.org/paper/396/
Let be a random polynomial such that ( ) is a sequence of mutually independent normally distributed random variables with mean zero and variance one; ( ) be a sequence of normalized Jacobi polynomials , orthogonal with respect to the interval (-1,1). It is proved that the average number of points of inflection of the random equation y=0 is asymptotic to .