Abstract
Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials B2k+1(x) and the Euler polynomials E2k+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.
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