Mean number of real zeros of a random trigonometric polynomial. III
1995 ◽
Vol 8
(3)
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pp. 299-317
Keyword(s):
The Mean
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If a1,a2,…,an are independent, normally distributed random variables with mean 0 and variance 1, and if vn is the mean number of zeros on the interval (0,2π) of the trigonometric polynomial a1cosx+2½a2cos2x+…+n½ancosnx, then vn=2−½{(2n+1)+D1+(2n+1)−1D2+(2n+1)−2D3}+O{(2n+1)−3}, in which D1=−0.378124, D2=−12, D3=0.5523. After tabulation of 5D values of vn when n=1(1)40, we find that the approximate formula for vn, obtained from the above result when the error term is neglected, produces 5D values that are in error by at most 10−5 when n≥8, and by only about 0.1% when n=2.
1997 ◽
Vol 10
(1)
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pp. 67-70
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1968 ◽
Vol 64
(3)
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pp. 721-730
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1997 ◽
Vol 10
(1)
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pp. 57-66
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1990 ◽
Vol 3
(4)
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pp. 253-261
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2018 ◽
Vol 20
(1)
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pp. 109-116
1995 ◽
Vol 58
(1)
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pp. 39-46
2006 ◽
Vol 2006
◽
pp. 1-6
1987 ◽
Vol 5
(4)
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pp. 379-386
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1966 ◽
Vol s3-16
(1)
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pp. 53-84
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