Real zeros of a random polynomial with Legendre elements
1997 ◽
Vol 10
(3)
◽
pp. 257-264
Keyword(s):
Let T0∗(x),T1∗(x),…,Tn∗(x) be a sequence of normalized Legendre polynomials orthogonal with respect to the interval (−1,1). The asymptotic estimate of the expected number of real zeros of the random polynomial g0T0∗(x)+g1T1∗(x)+…+gnTn∗(x) where gj, j=1,2,…,n are independent identically and normally distributed random variables with mean zero and variance one is known. The present paper considers the case when the means and variances of the coefficients are not all necessarily equal. It is shown that in general this expected number of real zeros is only dependent on variances and is independent of the means.
2001 ◽
Vol 14
(3)
◽
pp. 265-274
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1998 ◽
Vol 21
(2)
◽
pp. 347-350
2004 ◽
Vol 2004
(63)
◽
pp. 3389-3395
Keyword(s):
1999 ◽
Vol 22
(3)
◽
pp. 579-586
1997 ◽
Vol 10
(1)
◽
pp. 57-66
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2006 ◽
Vol 2006
◽
pp. 1-6
◽
2015 ◽
Vol 2015
◽
pp. 1-7
1995 ◽
Vol 58
(1)
◽
pp. 39-46
2011 ◽
Vol 55
(1)
◽
pp. 173-181
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