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An asymptotic expansion for the expected number of real zeros of a random polynomial. (English) Zbl 0656.60062
Let $$f(z)=\sum^{n}_{k=0}a_ kz^ k$$ be a random algebraic polynomial of degree n, where $$a_ k$$, $$k=0,1,2,...,n$$ are independent random variables normally distributed with mean zero and variance 1. Let E N(-$$\infty,\infty)$$ be the expected number of real zeros of f(z). Then an asymptotic expansion of E N(-$$\infty,\infty)$$ is of the form $E N(- \infty,\infty)=(2/\pi)\log (n+1)+\sum^{\infty}_{p=0}Ap(n+1)^{-p},$ in which $$A_ 0=0\cdot 625735818$$, $$A_ 1=0$$, $$A_ 2=-0\cdot 24261274$$, $$A_ 3=0$$, $$A_ 4=-0\cdot 08794067$$, $$A_ 5=0$$.
Reviewer: A.M.Sambandham

MSC:
 60G99 Stochastic processes
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References:
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