A matrix approach to the binomial theorem
نویسندگان
چکیده
منابع مشابه
determinant of the hankel matrix with binomial entries
abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.
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In this article, we demonstrate how the Binomial Theorem in turn arises from a one-parameter generalization of the Sierpinski triangle. The connection between them is given by the sum-of-digits function, s(k), defined as the sum of the digits in the binary representation of k (see [1]). For example, s(3) = s(1·2+1·2) = 2. Towards this end, we begin with a well-known matrix formulation of Sierpi...
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ژورنال
عنوان ژورنال: Ukrainian Mathematical Journal
سال: 2013
ISSN: 0041-5995,1573-9376
DOI: 10.1007/s11253-013-0752-3