Zobrazeno 1 - 10
of 443
pro vyhledávání: '"Maillard, J. M."'
This paper is a plea for diagonals and telescopers of rational, or algebraic, functions using creative telescoping, in a computer algebra experimental mathematics learn-by-examples approach. We show that diagonals of rational functions (and this is a
Externí odkaz:
http://arxiv.org/abs/2310.06963
Autor:
Boukraa, S., Maillard, J. -M.
This paper provides several illustrations of the numerous remarkable properties of the lambda-extensions of the two-point correlation functions of the Ising model, sheding some light on the non-linear ODEs of the Painlev\'e type. We first show that t
Externí odkaz:
http://arxiv.org/abs/2212.07984
Autor:
Boukraa, S., Maillard, J-M.
We revisit, with a pedagogical heuristic motivation, the lambda extension of the low-temperature row correlation functions C(M,N) of the two-dimensional Ising model. In particular, using these one-parameter series to understand the deformation theory
Externí odkaz:
http://arxiv.org/abs/2209.07434
We study the factorizations of Ising low-temperature correlations C(M,N) for $\nu=-k$ and M+N odd, $M \le N$, for both the cases $M\neq 0$ where there are two factors, and $M=0$ where there are four factors. We find that the two factors for $ M \neq
Externí odkaz:
http://arxiv.org/abs/2204.10096
We present Painlev{\'e} VI sigma form equations for the general Ising low and high temperature two-point correlation functions $ C(M,N)$ with $M \leq N $ in the special case $\nu = -k$ where $\nu = \, \sinh 2E_h/k_BT/\sinh 2E_v/k_BT$. More specifical
Externí odkaz:
http://arxiv.org/abs/2008.06912
We show that the results we had obtained on diagonals of nine and ten parameters families of rational functions using creative telescoping, yielding modular forms expressed as pullbacked $ _2F_1$ hypergeometric functions, can be obtained, much more e
Externí odkaz:
http://arxiv.org/abs/2002.00789
We show that the unresolved examples of Christol's conjecture $ \, _3F_{2}\left([2/9,5/9,8/9],[2/3,1],x\right)$ and $_3F_{2}\left([1/9,4/9,7/9],[1/3,1],x\right)$, are indeed diagonals of rational functions. We also show that other $\, _3F_2$ and $\,
Externí odkaz:
http://arxiv.org/abs/1912.10259
We provide a set of diagonals of simple rational functions of three and four variables that are squares of Heun functions. These Heun functions obtained through creative telescoping, turn out to be either pullbacked $_2F_1$ hypergeometric functions a
Externí odkaz:
http://arxiv.org/abs/1910.10761
Publikováno v:
Journal of Physics A: Mathematical and Theoretical, vol. 51, article 455201, 2018
We recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. We find that a seven-parameter rational function of three variables with a numerator equal to one (reciprocal of a polynomi
Externí odkaz:
http://arxiv.org/abs/1805.04711
Autor:
Abdelaziz, Y., Maillard, J. -M.
We show that non-linear Schwarzian differential equations emerging from covariance symmetry conditions imposed on linear differential operators with hypergeometric function solutions, can be generalized to arbitrary order linear differential operator
Externí odkaz:
http://arxiv.org/abs/1706.07423