Results 1 to 10 of about 165,496 (329)

Binomial Coefficients and Jacobi Sums [PDF]

Transactions of the American Mathematical Society, 1984
Throughout this paper e e denotes an integer ⩾ 3 \geqslant 3 and p p a prime ≡ 1   ( mod e ) \equiv \;1\ \pmod e . With f f defined by p = e f
Hudson, Richard H., Williams, Kenneth S.
openaire   +2 more sources

Many identities from one

Le Matematiche, 1996
We specialise an ingeniously contrived identity to obtain a plethora of startling combinatorial identities. Limiting cases include well known evaluations of ζ(2), ζ(4) and ζ(6).
Chu Wenchang
doaj  

An upper bound on binomial coefficients in the de Moivre – Laplace form

Журнал Белорусского государственного университета: Математика, информатика, 2022
We provide an upper bound on binomial coefficients that holds over the entire parameter range an whose form repeats the form of the de Moivre – Laplace approximation of the symmetric binomial distribution.
Sergey V. Agievich
doaj   +1 more source

Divisibility of binomial coefficients by powers of two

, 2017
For nonnegative integers $j$ and $n$ let $\Theta(j,n)$ be the number of entries in the $n$-th row of Pascal's triangle that are not divisible by $2^{j+1}$. In this paper we prove that the family $j\mapsto\Theta(j,n)$ usually follows a normal distribution.
Spiegelhofer, Lukas, Wallner, Michael
core   +2 more sources

Polynomial Triangles Revisited [PDF]

, 2012
A polynomial triangle is an array whose inputs are the coefficients in integral powers of a polynomial. Although polynomial coefficients have appeared in several works, there is no systematic treatise on this topic. In this paper we plan to fill this gap.
Mohammedia Morocco, Nour-eddine Fahssi
core  

Lucas' theorem: its generalizations, extensions and applications (1878--2014) [PDF]

, 2014
In 1878 \'E. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a prime, $n=n_0 ...
Meštrović, Romeo
core  

Three new classes of binomial Fibonacci sums [PDF]

Transactions on Combinatorics
In this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients. One particular result is linked to a problem proposal recently published in the journal The Fibonacci Quarterly.
Robert Frontczak
doaj   +1 more source

Congruences for central binomial sums and finite polylogarithms [PDF]

, 2011
We prove congruences, modulo a power of a prime p, for certain finite sums involving central binomial coefficients $\binom{2k}{k}$
Mattarei, Sandro, Tauraso, Roberto
core  

Applications of Lehmer’s Infinite Series Involving Reciprocals of the Central Binomial Coefficients

Journal of Function Spaces, 2022
The main objective of this paper is to establish several new closed-form evaluations of the generalized hypergeometric function Fq+1qz for q=2,3,4,5. This is achieved by means of separating the generalized hypergeometric function Fq+1qz (q=2,3,4,5) into ...
B. R. Srivatsa Kumar, Adem Kılıçman, Arjun K. Rathie   +2 more
doaj   +1 more source

Multiple sums for cyclically symmetric products of binomial coefficients

AIMS Mathematics
Carlitz' multiple sums involving cyclically symmetric products of binomial coefficients are extended by introducing weight monomials of $ m $-variables.
Marta Na Chen, Wenchang Chu
doaj   +1 more source