Zobrazeno 1 - 10
of 1 381
pro vyhledávání: '"11B65"'
Autor:
Akerele, Olofin, Adeshina, Quadri
We investigate a class of combinatorial sums involving reciprocals of central binomial coefficients , employing generating functions as the primary solution technique to formulate and analyze series involving the Catalan's constant. Using a direct ap
Externí odkaz:
http://arxiv.org/abs/2411.11884
Autor:
Guadalupe, Russelle
In this paper, we study the $5$-dissections of certain Ramanujan's theta functions, particularly $\psi(q)\psi(q^2), \varphi(-q)$ and $\varphi(-q)\varphi(-q^2)$, and derive an identity for $q(q;q)_{\infty}^6/(q^5;q^5)_{\infty}^6$ in terms of certain p
Externí odkaz:
http://arxiv.org/abs/2410.14149
Autor:
Da Conceição, Joaquim Cera
Publikováno v:
J. Integer Sequences 26 (2023) Article 23.9.7
We define a new generalization of Catalan numbers to multinomial coefficients. With arithmetic methods, we study their integrality and the integrality of their Lucasnomial generalization. We give a complete characterization of regular Lucas sequences
Externí odkaz:
http://arxiv.org/abs/2410.04857
Autor:
Maw, Aung Phone
We present outlines of a general method to reach certain kinds of $q$-multiple sum identities. Throughout our exposition, we shall give generalizations to the results given by Dilcher, Prodinger, Fu and Lascoux, Zeng, and Guo and Zhang concerning $q$
Externí odkaz:
http://arxiv.org/abs/2409.16330
Autor:
Sun, Zhi-Hong, Ye, Dongxi
Recently, using modular forms F. Beukers posed a unified method that can deal with a large number of supercongruences involving binomial coefficients and Ap\'ery-like numbers. In this paper, we use Beukers' method to prove some conjectures of the fir
Externí odkaz:
http://arxiv.org/abs/2408.09776
Autor:
López, Ronald Orozco
In this paper, we are mainly interested in using the $q$-exponential operator of Chen [8] in proving identities involving the generalized Rogers-Szeg\"o polynomials r$_{n}(x,b;q)$ of Saad [11], the $(s,t)$-derivatives of Partial Theta function $\Thet
Externí odkaz:
http://arxiv.org/abs/2408.08943
The summatory function of the number of binomial coefficients not divisible by a prime is known to exhibit regular periodic oscillations, yet identifying the less regularly behaved minimum of the underlying periodic functions has been open for almost
Externí odkaz:
http://arxiv.org/abs/2408.06817
We determine the higher weight spectra of $q$-ary Reed-Muller codes $C_q=RM_q(2,2)$ for all prime powers $q$. This is equivalent to finding the usual weight distributions of all extension codes of $C_q$ over every field extension of $F_q$ of finite d
Externí odkaz:
http://arxiv.org/abs/2408.02548
Autor:
Maw, Aung Phone
We provide an exposition of q-identities with multiple sums related to divisor functions given by Dilcher, Prodinger, Fu and Lascoux, Zeng, Guo and Zhang. Meanwhile, for each of these identities, a more powerful statement will be derived through our
Externí odkaz:
http://arxiv.org/abs/2408.00807
Autor:
Liu, Ji-Cai
In the proof of the irrationality of $\zeta(3)$ and $\zeta(2)$, Ap\'ery defined two integer sequences through $3$-term recurrences, which are known as the famous Ap\'ery numbers. Zagier, Almkvist--Zudilin and Cooper successively introduced the other
Externí odkaz:
http://arxiv.org/abs/2406.18059