Nonnegative linearization coefficients of the generalized Bessel polynomials
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In this work, we solve the general linearization problem for the generalized Bessel polynomials using their inversion formula. For some particular values, we get a recurrence relation satisfied by the linearization coefficients from which we deduce their nonnegativity. We also recover a result given by Berg and Vignat (Constr Approx 27:15–32, 2008) and derived an explicit formula that generalizes a result by Atia and Zeng (Ramanujan J 28:211–221, 2012).
KeywordsLinearization formula Multiplication formula Bessel polynomials Nonnegativity
Mathematics Subject Classification33C10 33C45
The author is grateful for the useful comments from the referee which improve considerably this manuscript.
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