Several conjectures posed by Qi on completely monotonic degrees of remainders for the asymptotic formulas of the digamma and trigamma functions are proved.

Starting from the definitions of the r-Whitney numbers of both kinds, in this paper we give two convolution formulas for the r-Whitney numbers. The convolution formula for the r-Whitney numbers of the second kind is new and it helps us to find the LU factorization of a new type of matrices consisting of the r-Whitney numbers of the second kind $W_{m,r}(s+i+j,s+j)$. Meanwhile, the evaluation of the determinant of this type of matrices is given. Finally, the Dobinski and Spivey types of identities for the r-Whitney numbers of the second kind are also presented.

By utilizing the generating function of higher-order Bernoulli polynomials, we uncover novel relationships that intertwine higher-order Bernoulli polynomials, higher-order Bernoulli numbers, Stirling numbers of the second kind, and central factorial numbers of the second kind. Leveraging these interconnections, we successfully rederive the identities formulated by Qi and Taylor, specifically those pertaining to Stirling numbers of the second kind and central factorial numbers of the second kind. Additionally, we derive series expansions for both positive integer and real powers of the sinc and sinhc functions.