The Lower Bound Estimation for the Number of Zeros of Random Transcendental Polynomial
Keywords:
Probability spaces, Characteristic function, Joint density function, Moment matrix, Exceptional set, Marginal frequency function, Distribution function.
Abstract
The object of this paper is to find a lower bound estimation for the number of zeros of the random transcendental equation nP v=0 dvξv (ω) zv = 0, subject to the condition that the coefficients are non-identically distributed dependent random variables. Throughout the paper n is considered to be very large and µ’s denote positive constants assuming different values in different occurrences.
References
E.A.Evans, On the number of a random algebraic equation, Proc. London Math. Soc., 3(15)(1965), 731-749.
G.Samal, Onthe number of real roots of a random algebraic equation, Proc. Cambridge Philos. Soc., 58(1962), 433-442.
G.Samal and M.N.Mishra, Onthe lower bound of the number of real roots of a randomalgebraic with infinite variance, Proc. Am. Math. Soc., 33(1972), 523-528.
M.Sambandham, On the upper bound of the number of real zeros of a random algebraicequation, J. Indian Math. Soc., 42(1978), 15-26.
G.Samal, Onthe number of real roots of a random algebraic equation, Proc. Cambridge Philos. Soc., 58(1962), 433-442.
G.Samal and M.N.Mishra, Onthe lower bound of the number of real roots of a randomalgebraic with infinite variance, Proc. Am. Math. Soc., 33(1972), 523-528.
M.Sambandham, On the upper bound of the number of real zeros of a random algebraicequation, J. Indian Math. Soc., 42(1978), 15-26.
How to Cite
Ajaya Kumar Singh. (2016). The Lower Bound Estimation for the Number of Zeros of Random Transcendental Polynomial. International Journal of Current Research in Science and Technology, 2(10), 1-7. Retrieved from https://crst.gfer.org/index.php/crst/article/view/73
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