Zobrazeno 1 - 10
of 362
pro vyhledávání: '"33F10"'
We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating functions, d
Externí odkaz:
http://arxiv.org/abs/2411.18362
Autor:
Straton, Jack C.
In a prior paper we found that the Fourier-Legendre series of a Bessel function of the first kind J_{N}\left(kx\right) and of a modified Bessel functions of the first kind I_{N}\left(kx\right) lead to an infinite set of series involving \,_{1}F_{2} h
Externí odkaz:
http://arxiv.org/abs/2412.00019
Autor:
Zhao, James Jing Yu
Baxter permutations arose in the study of fixed points of the composite of commuting functions by Glen Baxter in 1964. This type of permutations are counted by Baxter numbers $B_n$. It turns out that $B_n$ enumerate a lot of discrete objects such as
Externí odkaz:
http://arxiv.org/abs/2410.05031
We give a closed form for $quotients$ of truncated basic hypergeometric series where the base $q$ is evaluated at roots of unity.
Comment: $1+2+\dots+N = 1\cdot2\dotsb N$ pages
Comment: $1+2+\dots+N = 1\cdot2\dotsb N$ pages
Externí odkaz:
http://arxiv.org/abs/2406.02954
Autor:
Campbell, John M.
Chu and Zhang, in 2014, introduced hypergeometric transforms derived through the application of an Abel-type summation lemma to Dougall's ${}_{5}H_{5}$-series. These transforms were applied by Chu and Zhang to obtain accelerated rates of convergence,
Externí odkaz:
http://arxiv.org/abs/2405.02776
Autor:
Du, Hao, Raab, Clemens G.
In symbolic integration, the Risch--Norman algorithm aims to find closed forms of elementary integrals over differential fields by an ansatz for the integral, which usually is based on heuristic degree bounds. Norman presented an approach that avoids
Externí odkaz:
http://arxiv.org/abs/2404.13042
Autor:
Tabuguia, Bertrand Teguia
Take a multiplicative monoid of sequences in which the multiplication is given by Hadamard product. The set of linear combinations of interleaving monoid elements then yields a ring. For hypergeometric sequences, the resulting ring is a subring of th
Externí odkaz:
http://arxiv.org/abs/2404.10143
Autor:
Au, Kam Cheong
We point out a correspondence between many classical and $q$-hypergeometric Wilf-Zeilberger seeds, it enables us to find $q$-analogues of many classical hypergeometric series identities, and offers a conceptual explanation to why such $q$-analogue sh
Externí odkaz:
http://arxiv.org/abs/2403.04555
Autor:
Arreche, Carlos E., Sitaula, Hari P.
In 2012 Chen and Singer introduced the notion of discrete residues for rational functions as a complete obstruction to rational summability. More explicitly, for a given rational function f(x), there exists a rational function g(x) such that f(x) = g
Externí odkaz:
http://arxiv.org/abs/2402.07328
Autor:
Sun, Zhi-Wei, Zhou, Yajun
Using cyclotomic multiple zeta values of level $8$, we confirm and generalize several conjectural identities on infinite series with summands involving $\binom{2k}k8^k/(\binom{3k}k\binom{6k}{3k})$. For example, we prove that \[\sum_{k=0}^\infty\frac{
Externí odkaz:
http://arxiv.org/abs/2401.14197