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The expected value of the number of real zeros of a random sum of Legendre polynomials |
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| Authors: | J. Ernest Wilkins Jr. |
| Affiliation: | Department of Mathematics, Clark Atlanta University, Atlanta, Georgia 30314 |
| Abstract: | It is known that the expected number of zeros in the interval  of the sum  , in which  is the normalized Legendre polynomial of degree  and the coefficients  are independent normally distributed random variables with mean 0 and variance 1, is asymptotic to  for large  . We improve this result and show that this expected number is  for any positive  . |
| Keywords: | Real zeros random polynomials Legendre polynomials |
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