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We consider the Touchard polynomials, which are extensions of the Bell polynomials, and the P-polynomials which, together with the Touchard polynomials, form a quasi-orthogonal system. We establish analytical conjugacy of the Touchard polynomials and the P-polynomials, which allows us, in particular, to find a series of new recurrence relations for the P-polynomials.

On analytical conjugacy of Ton chard polynomials and the polynomials quasi-orthogonal to them