Mean number of real zeros of a random trigonometric polynomial

Author:
J. Ernest Wilkins

Journal:
Proc. Amer. Math. Soc. **111** (1991), 851-863

MSC:
Primary 60G99

DOI:
https://doi.org/10.1090/S0002-9939-1991-1039266-0

MathSciNet review:
1039266

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If are independent, normally distributed random variables with mean 0 and variance 1, and if is the mean value of the number of zeros on the interval of the trigonometric polynomial , then

**[1]**M. Abramowitz and I. A. Stegun, eds.,*Handbook of mathematical functions, with formulas, graphs and mathematical tables*, Wiley, New York, 1972.**[2]**A. T. Bharucha-Reid and M. Sambandham,*Random polynomials*, Probability and Mathematical Statistics, Academic Press, Inc., Orlando, FL, 1986. MR**856019****[3]**M. J. Christensen and M. Sambandham,*Improved estimates for real roots of random trigonometric polynomials*, unpublished manuscript.**[4]**Harald Cramér and M. R. Leadbetter,*Stationary and related stochastic processes. Sample function properties and their applications*, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR**0217860****[5]**Minaketan Das,*The average number of real zeros of a random trigonometric polynomial.*, Proc. Cambridge Philos. Soc.**64**(1968), 721–729. MR**0233398****[6]**Harold T. Davis,*The summation of series*, The Principia Press of Trinity University, San Antonio, Tex., 1962. MR**0141908****[7]***Bessel functions. Part III: Zeros and associated values*, Royal Society Mathematical Tables, Vol. 7. Prepared under the direction of the Bessel Functions Panel of the Mathematical Tables Committee, Cambridge University Press, New York, 1960. MR**0119441****[8]**E. T. Whittaker and G. N. Watson,*A course of modern analysis*(American ed.), MacMillan, New York, 1943.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
60G99

Retrieve articles in all journals with MSC: 60G99

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1039266-0

Article copyright:
© Copyright 1991
American Mathematical Society