The zeros on complex differential-difference polynomials of certain types
نویسندگان
چکیده
منابع مشابه
The Zeros of Certain Composite Polynomials
we may obtain various theorems on the relative location of the zeros of A 0(2) and An(z) by the familiar method of first finding such relations for two successive Ak{z) and then iterating the relations n times. This method has already been employed in the study of the zeros of sequence (1.1) for the following three cases: (1) for all k, Pk = 0 and yk is real; 1 (2) for all k, yk~m + l—a limitin...
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In order that <r0 ^ 0 , in which case (3.1) will converge in the right half of the s-plane, it is sufficient that vn tend to infinity faster than log n. The argument used to complete the proof of Theorem 2 is the same as the one used above in connection with Theorem 1. Notice that if {vn+i — vn} is not a null sequence, then vn tends to infinity faster than log n. This eliminates the extra restr...
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Mark Kac gave an explicit formula for the expectation of the number, vn (a), of zeros of a random polynomial, n-I Pn(z) = E ?tj, j=O in any measurablc subset Q of the reals. Here, ... ?In-I are independent standard normal random variables. In fact, for each n > 1, he obtained an explicit intensity function gn for which E vn(L) = Jgn(x) dx. Here, we extend this formula to obtain an explicit form...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2018
ISSN: 1687-1847
DOI: 10.1186/s13662-018-1712-x