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* If [[mu].sub.n] = [B.sub.n], the number of partitions of [n], then [b.sub.n] = n + 1 and [[lambda].sub.n] = n; the corresponding polynomials are Charlier polynomials (with a = 1) .
Letting k go from 0 to infinity would then allow us to interpolate between Chebyshev polynomials and Hermite polynomials; using NC [P.sub.k](n) would give the corresponding interpolation between shifted Chebyshev and Charlier polynomials.
(x - n + 1) [sigma] (X) = 1 translated Charlier polynomials [sigma] (x) = x falling factorials, Charlier, Meixner, Krawtchouk polynomials deg([sigma](x), x) = 2 Hahn polynomials
For example, let's consider the Charlier polynomials and their associated.
SUSLOV, The q-harmonic oscillator and an analogue of the Charlier polynomials
In section 3 the factorization of the hypergeometric-type difference equation is discussed, which is used in section 4 to construct a dynamical symmetry algebra in the case of the Charlier polynomials. In section 5 the Kravchuk and the Meixner cases are considered in detail.
and [alpha] = 0, i.e., the Charlier polynomials. Moreover, in this case [[lambda].sub.n] = n.
Charlier polynomials. From the generating function of the Charlier polynomials we have:
The theory developed here may be extended to the case: any polynomial [right arrow] Charlier polynomial .