Algebraic polynomials with random coefficients
2002 ◽
Vol 15
(1)
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pp. 83-88
Keyword(s):
This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a0(ω)+a1(ω)(n1)1/2x+a2(ω)(n2)1/2x2+…an(ω)(nn)1/2xn when n is large. The coefficients {aj(w)}j=0n, w∈Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space (A,Ω,Pr). A special case of dependent coefficients is also studied.
2015 ◽
Vol 2015
◽
pp. 1-7
1999 ◽
Vol 22
(3)
◽
pp. 579-586
1998 ◽
Vol 21
(2)
◽
pp. 347-350
2008 ◽
Vol 85
(1)
◽
pp. 81-86
◽
2004 ◽
Vol 2004
(63)
◽
pp. 3389-3395
Keyword(s):
2008 ◽
Vol 2008
◽
pp. 1-8
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2006 ◽
Vol 2006
◽
pp. 1-6
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2001 ◽
Vol 14
(3)
◽
pp. 265-274
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1997 ◽
Vol 10
(3)
◽
pp. 257-264
1995 ◽
Vol 58
(1)
◽
pp. 39-46