Zobrazeno 1 - 10
of 316
pro vyhledávání: '"James, MC"'
Autor:
Archibald, DW, James, MC
Publikováno v:
Endangered Species Research, Vol 37, Pp 149-163 (2018)
Identification and understanding of various patterns of injury in marine species such as cetaceans and sea turtles can elucidate corresponding threats and inform conservation efforts. Here we used standardized external injury assessments to investiga
Externí odkaz:
https://doaj.org/article/22fe80f5909f4e59bb9c62249f3ea0b9
Publikováno v:
The Journal of Mathematical Analysis and Applications Volume 447, Issue 2, 15 March 2017, Pages 1126-1141
In this paper we show that various continued fractions for the quotient of general Ramanujan functions $G(aq,b,\l q)/G(a,b,\l)$ may be derived from each other via Bauer-Muir transformations. The separate convergence of numerators and denominators pla
Externí odkaz:
http://arxiv.org/abs/1906.11991
Autor:
Laughlin, James Mc
Publikováno v:
Analytic number theory, modular forms and q-hypergeometric series, 503-531, Springer Proc. Math. Stat., 221, Springer, Cham, 2017
The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of $_2\psi_2$ series \[ \sum_{n=-\infty}^{\infty}\frac{(a,c;q)_n}{(b,d;q)_n}z^n. \] Three transformation fo
Externí odkaz:
http://arxiv.org/abs/1906.11997
Autor:
Laughlin, James Mc
Andrews and Bressoud, Alladi and Gordon, and others, have proven, in a number of papers, that the coefficients in various arithmetic progressions in the series expansions of certain infinite $q$-products vanish. In the present paper it is shown that
Externí odkaz:
http://arxiv.org/abs/1906.11978
Autor:
Laughlin, James Mc, Sills, Andrew V.
Publikováno v:
Annals of Combinatorics Volume 16, Number 3 (2012), 591-607
Using a pair of two variable series-product identities recorded by Ramanujan in the lost notebook as inspiration, we find some new identities of similar type. Each identity immediately implies an infinite family of Rogers-Ramanujan type identities, s
Externí odkaz:
http://arxiv.org/abs/1901.05326
Autor:
Laughlin, James Mc
Publikováno v:
J. Aust. Math. Soc. 98 (2015), no. 1, 69-77
We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if \begin{equation*} \frac{(q^{r-tk}, q^{mk-(r-tk)}; q^{mk})_\infty}{(q^r,q^{mk-r}; q^{
Externí odkaz:
http://arxiv.org/abs/1901.04835
Autor:
Laughlin, James Mc, Zimmer, Peter
Publikováno v:
The Ramanujan Journal Volume 28, Number 2 (2012), 155-173
We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new su
Externí odkaz:
http://arxiv.org/abs/1901.02872
Autor:
Laughlin, James Mc
Publikováno v:
INTEGERS: The Electronic Journal of Combinatorial Number Theory 16 (2016), A66, 11 pp
In the present paper we initiate the study of a certain kind of partition inequality, by showing, for example, that if $M\geq 5$ is an integer and the integers $a$ and $b$ are relatively prime to $M$ and satisfy $1\leq a
Externí odkaz:
http://arxiv.org/abs/1901.01993
Autor:
Laughlin, James Mc
Publikováno v:
The Ramanujan Journal April 2016, Volume 39, Issue 3, pp 545-565
We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence $\{g(k)\}$), to be reduced to an infinite $q$-product times a single basic hypergeometri
Externí odkaz:
http://arxiv.org/abs/1901.01988
Autor:
Laughlin, James Mc
Publikováno v:
Applicable Analysis and Discrete Mathematics (AADM) 5 (2011), 67-79
Let $(\alpha_n(a,k),\beta_n(a,k))$ be a WP-Bailey pair. Assuming the limits exist, let \[ (\alpha_n^*(a),\beta_n^*(a))_{n\geq 1} = \lim_{k \to 1}\left(\alpha_n(a,k),\frac{\beta_n(a,k)}{1-k}\right)_{n\geq 1} \] be the \emph{derived} WP-Bailey pair. By
Externí odkaz:
http://arxiv.org/abs/1901.05886