Numerical problems with the Pascal triangle in moment computation
نویسندگان
چکیده
منابع مشابه
Fermat Numbers in the Pascal Triangle
For any positive integer m let Fm = 2 2 + 1 be the mth Fermat number. In this short note we show that the only solutions of the diophantine equation Fm = ( n k ) are the trivial ones, i.e., those with k = 1 or n− 1.
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for 0 ≤ i, j ∈ N. The matrix P is hence the famous Pascal triangle yielding the binomial coefficients and can be recursively constructed by the rules p0,i = pi,0 = 1 for i ≥ 0 and pi,j = pi−1,j + pi,j−1 for 1 ≤ i, j. In this paper we are interested in (sequences of determinants of finite) matrices related to P . The present section deals with determinants of some minors of the above Pascal tria...
متن کاملMatrices Related to the Pascal Triangle
for 0 ≤ i, j ∈ N. The matrix P is hence the famous Pascal triangle yielding the binomial coefficients and can be recursively constructed by the rules p0,i = pi,0 = 1 for i ≥ 0 and pi,j = pi−1,j + pi,j−1 for 1 ≤ i, j. In this paper we are interested in (sequences of determinants of finite) matrices related to P . The present section deals with some minors (determinants of submatrices) of the abo...
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It is the purpose of this article to present a triangular array of numbers similar to Pascal’s triangle and to prove a corresponding criterion for the twin prime pairs. A further goal is to place all this in the context of some classical orthogonal polynomials and to relate it to some recent work of John D’Angelo. To begin, and for the sake of completeness, we present a short proof of the Pasca...
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À quoi reconnâıt-on qu’une suite est plus ou moins “compliquée” ? Une des traductions mathématiques de ce terme vague consiste à compter les facteurs ou blocs qui apparaissent dans cette suite, (voir par exemple [2]). Il y a naturellement bien d’autres approches possibles, qui dépendent en particulier à la fois des applications qu’on a à l’esprit ... et des quantités que l’on sait calculer ou e...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2016
ISSN: 0377-0427
DOI: 10.1016/j.cam.2016.03.033