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1: 24.18 Physical Applications
Euler polynomials also appear in statistical physics as well as in semi-classical approximations to quantum probability distributions (Ballentine and McRae (1998)).
2: 18.2 General Orthogonal Polynomials
Then the OP’s are called semi-classical and (18.2.44) is called a structure relation. …
3: Bibliography M
  • A. P. Magnus (1995) Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials. J. Comput. Appl. Math. 57 (1-2), pp. 215–237.