Results 11 to 20 of about 44,005 (262)

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, Dae San Kim, Hyunseok Lee, Jongkyum Kwon   +3 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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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, Robert Frontczak, Taras Goy   +2 more
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Evaluation of a Special Hankel Determinant of Binomial Coefficients [PDF]

Discrete Mathematics & Theoretical Computer Science, 2008
This paper makes use of the recently introduced technique of $\gamma$-operators to evaluate the Hankel determinant with binomial coefficient entries $a_k = (3 k)! / (2k)! k!$. We actually evaluate the determinant of a class of polynomials $a_k(x)$ having
Ömer Eugeciouglu, Timothy Redmond, Charles Ryavec   +2 more
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Some properties of binomial coefficients and their application to growth modelling

Arab Journal of Basic and Applied Sciences, 2018
Some properties of diagonal binomial coefficients were studied in respect to frequency of their units’ digits. An approach was formulated that led to the use of difference tables to predict if certain units’ digits can appear in the values of binomial ...
Vladimir L. Gavrikov
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Euler-type sums involving multiple harmonic sums and binomial coefficients

Open Mathematics, 2021
In this paper, we mainly show that generalized Euler-type sums of multiple harmonic sums with reciprocal binomial coefficients can be expressed in terms of rational linear combinations of products of classical multiple zeta values (MZVs) and multiple ...
Si Xin
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Fractional Sums and Differences with Binomial Coefficients

Discrete Dynamics in Nature and Society, 2013
In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives.
Thabet Abdeljawad, Dumitru Baleanu, Fahd Jarad, Ravi P. Agarwal   +3 more
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ON DIVISIBILITY OF BINOMIAL COEFFICIENTS [PDF]

Journal of the Australian Mathematical Society, 2012
AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.
openaire   +1 more source

Infinite series containing quotients of central binomial coefficients [PDF]

Notes on Number Theory and Discrete Mathematics
By making use of the Wallis' integral formulae and integration by parts, two classes of infinite series are evaluated, in closed form, in terms of π and Riemann zeta function.
Zhiling Fan
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Some combinatorial identities containing central binomial coefficients or Catalan numbers*

Applied Mathematics in Science and Engineering, 2023
In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four ...
Feng Qi, Da-Wei Niu, Dongkyu Lim
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