The theory of orthogonal polynomials started with analytic continued fractions going back to Euler, Gauss, Jacobi, Stieltjes… The combinatorial interpretations started in the late 70’s and is an active research domain. I will give the basis of the theory interpreting the moments of general (formal) orthogonal polynomials, Jacobi continued fractions and Hankel determinants with some families of weighted paths. In a second part I will give some examples of interpretations of classical orthogonal polynomials and of their moments (Hermite, Laguerre, Jacobi, …) with their connection to theoretical physics.

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Last updated: 16 Jan 2020