Average Number of Points of Inflection of a random sum of orthogonal polynomials

AUTHOR AND
AFFILIATION

1LOKANATH SAHOO and 2MINAKETAN MAHANTI
1Gopobandhu Science College, Athgarh, Cuttack,Odisha Pin-754029 (INDIA)
2College of Basic Science and Humanities, Orissa University of Agriculture and Technology,Bhubaneswar, Odisha (INDIA)
Email :minaketan_mahanti@yahoo.com Email :lokanath.math@gmail.com

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 .