Binomial coefficient

Ebook Concrete mathematics: A foundation for computer science (Second edition) presents the following content: Chapter 1: recurrent problems, chapter 2: sums, chapter 3: integer functions, chapter 4: number theory, chapter 5: binomial coefficients, chapter 6: special numbers, chapter 7: generating functions, chapter 8: discrete probability, chapter 9: asymptotics.

692p zizaybay1103 29-05-2024 8 2   Download

Part 1 of ebook "Proofs from the book" provides readers with contents including: number theory; geometry; six proofs of the infinity of primes; bertrand’s postulate; binomial coefficients are (almost) never powers; representing numbers as sums of two squares; the law of quadratic reciprocity; every finite division ring is a field; hilbert’s third problem - decomposing polyhedra; lines in the plane and decompositions of graphs; the slope problem;...

126p hanlinhchi 29-08-2023 6 2   Download

Heritability of a phenotypic or molecular trait measures the proportion of variance that is attributable to genotypic variance. It is an important concept in breeding and genetics. Few methods are available for calculating heritability for traits derived from high-throughput sequencing.

16p vioklahoma2711 19-11-2020 8 1   Download

This lesson introduces you to some of the most commonly used types of application software the programs that millions of people use each day to accomplish routine tasks. Although you might think of a computer as being a highly specialized machine, in fact it is most often used for basic, everyday tasks at home, school, and work. By applying computers and application programs to these mundane tasks, people can be more productive, creative, and efficient.

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The reciprocal super Catalan matrix studied by Prodinger is further generalized, introducing two additional parameters. Explicit formulae are derived for the LU -decomposition and their inverses, as well as the Cholesky decomposition.

13p danhdanh27 07-01-2019 19 1   Download

Sums of products of two Gaussian q -binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting applications of these results to certain generalized Fibonomial and Lucanomial sums are provided.

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By means of the hypergeometric series approach, we present a new proof of Sun’s conjecture on trigonometric series, which is simpler than the original one due to Sun and Meng. Several further infinite series identities are shown as examples.

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While the (common) value of the two determinants is symmetric in v and w, and in x and y, unlike the Jacobi-Trudi and N¨agelsbach-Kostka determinants, it is not symmetric in all four variables, much less in v, w, x, y, and z. The purpose of this article is to introduce p-Stirling numbers of the first and second kinds.

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Tuyển tập các báo cáo nghiên cứu khoa học hay nhất của tạp chí toán học quốc tế đề tài: A BINOMIAL COEFFICIENT IDENTITY ASSOCIATED TO A CONJECTURE OF BEUKERS...

1p thulanh4 11-09-2011 50 1   Download

Special Constants - Special Products and Factors - The binomial formula and binomiel coefficients

30p thachsaudoi 23-12-2009 87 16   Download

Science is what we understand well enough to explain to a computer. Art is everything else we do. During the past several years an important part of mathematics has been transformed from an Art to a Science: No longer do we need to get a brilliant insight in order to evaluate sums of binomial coefficients, and many similar formulas that arise frequently in practice; we can now follow a mechanical procedure and discover the answers quite systematically.

222p ledung 13-03-2009 141 14   Download