Results 11 to 20 of about 94,783 (262)

Annamalai’s  Binomial Identity and Theorem             [PDF]

SSRN Electronic Journal, 2022
This paper presents Annamalai’s binomial theorem, coefficient and identity generated by Chinnaraji Annamalai of the Indian Institute of Technology Kharagpur. Also, an extended geometric series is introduced with innovative summation of single terms and more successive terms of the series in this article.
Chinnaraji Annamalai
openaire   +2 more sources

A matrix approach to the binomial theorem [PDF]

Ukrainian Mathematical Journal, 2013
Motivated by the formula $$ {x^n}=\sum\limits_{k=0}^n {\left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array}} \right){{{\left( {x-1} \right)}}^k},} $$ we investigate factorizations of the lower-triangular Toeplitz matrix with (i; j )th entry equal to x
Stefan Stanimirović
openaire   +4 more sources

Polynomials of binomial type and Lucas’ Theorem [PDF]

Proceedings of the American Mathematical Society, 2015
At the intersection of number theory, commutative algebra and combinatorics. The new version has additional references.
David A. Goss
  +7 more sources

Construction of Novel Binomial Theorem [PDF]

, 2022
Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and combinatorial equations for solving today’s scientific problems and challenges. This paper presents a new binomial expansion and theorem. This idea can enable the scientific researchers to solve the real life problems.
Chinnaraji Annamalai
openaire   +2 more sources

Explicit constants in the nonuniform local limit theorem for Poisson binomial random variables [PDF]

Journal of Inequalities and Applications
In a recent paper the authors proved a nonuniform local limit theorem concerning normal approximation of the point probabilities P ( S = k ) $P(S=k)$ when S = ∑ i = 1 n X i $S=\sum_{i=1}^{n}X_{i}$ and X 1 , X 2 , … , X n $X_{1},X_{2},\ldots ,X_{n}$ are ...
Graeme Auld, Kritsana Neammanee
doaj   +2 more sources

Generalized Barred Preferential Arrangements [PDF]

Transactions on Combinatorics, 2023
We investigate a generalization of Fubini numbers. We present the combinatorial interpretation as barred preferential arrangements with some additional conditions on the blocks. We provide a proof for a generalization of Nelsen's Theorem.
José A. Adell, Beáta Bényi, Venkat Murali, Sithembele Nkonkobe   +3 more
doaj   +1 more source

A Neutrosophic Binomial Factorial Theorem with their Refrains [PDF]

Neutrosophic Sets and Systems, 2016
The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy.
Huda E. Khalid, Florentin Smarandache, Ahmed K. Essa   +2 more
doaj   +1 more source

On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics, 2021
We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in ...
Irina Shevtsova, Mikhail Tselishchev
doaj   +1 more source

A Rényi-Type Limit Theorem on Random Sums and the Accuracy of Likelihood-Based Classification of Random Sequences with Application to Genomics

Mathematics, 2023
We study classification of random sequences of characters selected from a given alphabet into two classes characterized by distinct character selection probabilities and length distributions.
Leonid Hanin, Lyudmila Pavlova
doaj   +1 more source

Two generalisations of the Binomial theorem

, 2005
5 pages, no figures. Accepted for publication in the Aust. Math.
Sacha C. Blumen
openaire   +4 more sources