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Some identities for a sequence of unnamed polynomials connected with the Bell polynomials

2018; Springer Science+Business Media; Volume: 113; Issue: 2 Linguagem: Inglês

10.1007/s13398-018-0494-z

1579-1505

Feng Qi, Da‐Wei Niu, Bai‐Ni Guo,

Nonlinear Waves and Solitons

In the paper, by virtue of (1) the Stirling inversion theorem and the binomial inversion theorem, (2) the Faà di Bruno formula and two identities for the Bell polynomials of the second kind, (3) a formula of higher order derivative for the ratio of two differentiable functions, the authors (1) present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, (2) derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, (3) recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.