Results 11 to 20 of about 46,123 (300)
On Binomial coefficients of real arguments
CoRR, 2022 6 ...
Fedoryaeva, Tatiana I.
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A sum of binomial coefficients [PDF]
Mathematics of Computation, 1978 An explicit expression is derived for the sum of the ( k + 1 ) (k + 1) st binomial coefficients in the nth, ( n − m ) (n - m) th, ( n − 2 m ) (n - 2m) th,... row of the arithmetic triangle.
Lajos Takács
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On divisibility of binomial coefficients
Discrete Mathematics, 1994 Let \(p\) be a prime and \(A(n,p)\) the \(p^ n\times p^ n\)-matrix with entries \(a_{ij}= \left(\begin{smallmatrix} i\\ j\end{smallmatrix}\right)\text{ mod }p\) for \(0\leq i,j< p^ n\). It is shown that \(A(n,p)\) is the \(n\)-fold tensor product of \(A(1,p)\) with itself. As an application a short proof is given that there are precisely \(\left(\begin{
Razpet, Marko
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On sums of binomial coefficients [PDF]
Proyecciones (Antofagasta)We investigate the integral representation of infinite sums involving the ratio of binomial coefficients. We also recover some wellknown properties of ζ (3) and extend the range of results given by other authors.
Sofo, Anthony
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Binomial Coefficients of Multidimensional Arrays [PDF]
Motivated by Parikh matrices of picture arrays introduced in combinatorial image analysis, we propose a generalization of binomial coefficients of words to multidimensional arrays. These coefficients recursively count prescribed patterns occurring in an array. The base case is the one of binomial coefficients of words.
Golafshan, Mohammadmehdi, Rigo, Michel
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Some identities of Gaussian binomial coefficients [PDF]
, 2023 In this paper, we present some identities of Gaussian binomial coefficients with respect to recursive sequences, Fibonomial coefficients, and complete functions by use of their ...
Shiue, Peter J.-S. +2 more
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Generalized double Fibonomial numbers
Ratio Mathematica, 2021 From the beginning of 20th century, generalization of binomial coefficient has been deliberated broadly. One of the most famous generalized binomial coefficients are Fibonomial coefficients, obtained by substituting Fibonacci numbers in place of natural ...
Mansi Shah, Shah Devbhadra
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Degenerate binomial coefficients and degenerate hypergeometric functions
Advances in Difference Equations, 2020 In this paper, we investigate degenerate versions of the generalized pth order Franel numbers which are certain finite sums involving powers of binomial coefficients.
Taekyun Kim +3 more
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Binomial Sum Relations Involving Fibonacci and Lucas Numbers
AppliedMath, 2023 In this paper, we provide a first systematic treatment of binomial sum relations involving (generalized) Fibonacci and Lucas numbers. The paper introduces various classes of relations involving (generalized) Fibonacci and Lucas numbers and different ...
Kunle Adegoke +2 more
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Binomial coefficients and applications
, 2023 U radu proučavamo binomne koeficijente, njihova svojstva i primjene te istražujemo vezu binomnih koeficijenata s raznim matematičkim pojmovima i rezultatima poput binomnog teorema, binomne razdiobe i pravila za računanje derivacija umnoška dviju funkcija.
Zajec, Jurica
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