Results 11 to 20 of about 56,637 (162)
Catalan–Qi Numbers, Series Involving the Catalan–Qi Numbers and a Hankel Determinant Evaluation
Journal of Mathematics, 2020 In this paper, using a study of the polynomial of Jacobi, we give an evaluation of the Hankel determinants that are associated with the sequence of Catalan–Qi numbers and several sequences of series involving the Catalan–Qi numbers.
Wathek Chammam
doaj +1 more source
Generalized $q,t$-Catalan numbers [PDF]
, 2020 Recent work of the first author, Negut and Rasmussen, and of Oblomkov and Rozansky in the context of Khovanov--Rozansky knot homology produces a family of polynomials in $q$ and $t$ labeled by integer sequences.
Gorsky, Eugene +3 more
core +4 more sources
On a Family of Infinite Series with Reciprocal Catalan Numbers
Axioms, 2022 We study a certain family of infinite series with reciprocal Catalan numbers. We first evaluate two special candidates of the family in closed form, where we also present some Catalan–Fibonacci relations.
Kunle Adegoke +2 more
doaj +1 more source
Three Identities of the Catalan-Qi Numbers
Mathematics, 2016 In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternative proofs of two identities of the Catalan numbers. The three identities of the Catalan-Qi numbers generalize three identities of the Catalan numbers.
Mansour Mahmoud, Feng Qi
doaj +1 more source
Dirichlet series and series with Stirling numbers
Cubo, 2023 This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbers ...
Khristo Boyadzhiev
doaj +1 more source
Some Properties of the Fuss–Catalan Numbers
Mathematics, 2018 In the paper, the authors express the Fuss⁻Catalan numbers as several forms in terms of the Catalan⁻Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the ...
Feng Qi, Pietro Cerone
doaj +1 more source
Some structures of the catalan numbers I [PDF]
ریاضی و جامعهThe Catalan numbers are ubiquitous in counting problems which is one of the primary reasons for its popularity. From various sources like books and Wikipedia we see that in combinatorial mathematics.
Daniel Yaqubi, Madjid Mirzavaziri
doaj +1 more source
A note on super Catalan numbers [PDF]
, 2012 We show that the super Catalan numbers are special values of the Krawtchouk polynomials by deriving an expression for the super Catalan numbers in terms of a signed set.Comment: 4 pages. Revised and Accepted.
Georgiadis, Evangelos +2 more
core +3 more sources
A New Approach to k-Jacobsthal Lucas Sequences
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2021 In this study, 〖CS〗_(k,n) of S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas sequences is defined. S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas S_(k,n) sequences is obtained.In addition the transformation of CS_(k,n) is written as the ...
Hakan Akkuş +2 more
doaj +1 more source