论文标题
某些Bernoulli和Euler多项式的正交多项式和Hankel决定因素
Orthogonal polynomials and Hankel Determinants for certain Bernoulli and Euler Polynomials
论文作者
论文摘要
利用某些Polygamma作为主要工具的持续分数扩展，我们发现与奇数索引bernoulli polyenmials $ b_ {2k+1}（x）$和Euler polynomials $ e_ e_ {2k+c+nmials $ e_ {2k+ν}（x）$，$ c $ c $ c $ c $ c $ c $ c $ c c $ c c $ c $ c。在此过程中，我们还确定了相应的雅各比持续分数（或j-fractions）和汉克尔的决定因素。在所有这些情况下，汉克尔的决定因素是$ x $的多项式，这完全超过了理由。
Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials $B_{2k+1}(x)$ and the Euler polynomials $E_{2k+ν}(x)$, for $ν=0, 1, 2$. In the process we also determine the corresponding Jacobi continued fractions (or J-fractions) and Hankel determinants. In all these cases the Hankel determinants are polynomials in $x$ which factor completely over the rationals.
