Mean number of real zeros of a random trigonometric polynomial IV

[摘要] Ifaj(j=1,2,…,n)are independent, normally distributed random variables with mean0and variance1, ifpis one half of any odd positive integer except one, and ifvnpis the mean number of zeros on(0,2π)of the trigonometric polynomiala1cosx+2pa2cos2x+…+npancosnx, thenvnp=μp{(2n+1)+D1p+(2n+1)−1D2p+(2n+1)−2D3p}+O{(2n+1)−3}, in whichμp={(2p+1)/(2p+3)}½, andD1p,D2pandD3pareexplicitly stated constants.

[学科分类] 应用数学