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Autor:
Stenlund, David, Wan, James G.
In this paper we discuss a class of double sums involving ratios of binomial coefficients. The sums are of the form \[ \sum_{j=0}^{n} \sum_{i=0}^j \frac{\binom{f_1(n)}{i}}{\binom{f_2(n)}{j}}\,c^{i-j}, \] where $f_1, f_2$ are functions of $n$. Such su
Externí odkaz:
http://arxiv.org/abs/1809.09634
Publikováno v:
Analytic Number Theory, Modular Forms and q-Hypergeometric Series (G.E. Andrews and F. Garvan, eds.), Springer Proceedings in Mathematics and Statistics 221 (Springer, 2018), pp. 179--205
We adopt the "translation" as well as other techniques to express several identities conjectured by Z.-W. Sun in arXiv:1102.5649v47 by means of known formulas for $1/\pi$ involving Domb and other Ap\'ery-like sequences.
Comment: 23 pages
Comment: 23 pages
Externí odkaz:
http://arxiv.org/abs/1512.04608
Autor:
Wan, James G.
We present a new method for producing series for $1/\pi$ and other constants using Legendre's relation, starting from a generation function that can be factorised into two elliptic $K$'s; this way we avoid much of modular theory or creative telescopi
Externí odkaz:
http://arxiv.org/abs/1302.5984
Publikováno v:
Journal of Organizational Change Management, 2019, Vol. 33, Issue 1, pp. 114-126.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/JOCM-10-2018-0288
Autor:
Wan, James
We present a unified approach which gives completely elementary proofs of three weighted sum formulae for double zeta values. This approach also leads to new evaluations of sums relating to the harmonic numbers, the alternating double zeta values, an
Externí odkaz:
http://arxiv.org/abs/1206.2424
We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in "Log-sine evaluations of Mahler measures" and "Special values of generalized log-sine integrals" by two of the authors. This motivates a detailed s
Externí odkaz:
http://arxiv.org/abs/1103.3035
Publikováno v:
Canad. J. Math. 64:5 (2012) 961--990
We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As one of the main results, we obtain a hypergeometric representation of th
Externí odkaz:
http://arxiv.org/abs/1103.2995
Autor:
Wan, James
We consider the moments of products of complete elliptic integrals of the first and second kinds. In particular, we derive new results using elementary means, aided by computer experimentation and a theorem of W. Zudilin. Diverse related evaluations,
Externí odkaz:
http://arxiv.org/abs/1101.1132