Mean number of real zeros of a random trigonometric polynomial IV
1997 ◽
Vol 10
(1)
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pp. 67-70
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Keyword(s):
The Mean
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If aj(j=1,2,…,n) are independent, normally distributed random variables with mean 0 and variance 1, if p is one half of any odd positive integer except one, and if vnp is the mean number of zeros on (0,2π) of the trigonometric polynomial a1cosx+2pa2cos2x+…+npancosnx, then vnp=μp{(2n+1)+D1p+(2n+1)−1D2p+(2n+1)−2D3p}+O{(2n+1)−3}, in which μp={(2p+1)/(2p+3)}½, and D1p, D2p and D3p are explicitly stated constants.
1995 ◽
Vol 8
(3)
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pp. 299-317
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
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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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