中文

Differential equation for Jacobi-Pineiro polynomials

量子代数 2007-05-23 v3

摘要

For rZ0r\in \Z_{\geq 0}, we present a linear differential operator %(\di)r+1+a1(x)(\di)r+...+ar+1(x)(\di)^{r+1}+ a_1(x)(\di)^{r}+...+a_{r+1}(x) of order r+1r+1 with rational coefficients and depending on parameters. This operator annihilates the rr-multiple Jacobi-Pi\~neiro polynomial. For integer values of parameters satisfying suitable inequalities, it is the unique Fuchsian operator with kernel consisting of polynomials only and having three singular points at x=0,1,x=0, 1, \infty with arbitrary non-negative integer exponents 0,m1+1,>...,m1+...+mr+r0, m_1+1, >..., m_1+...+m_r+r at x=0x=0, special exponents 0,k+1,k+2,...,k+r0, k+1, k+2,..., k+r at x=1x=1 and arbitrary exponents at x=x=\infty.

关键词

引用

@article{arxiv.math/0511138,
  title  = {Differential equation for Jacobi-Pineiro polynomials},
  author = {E. Mukhin and A. Varchenko},
  journal= {arXiv preprint arXiv:math/0511138},
  year   = {2007}
}

备注

Latex, 9 pages, revised version, misprints are corrected