  The main purpose of this paper is to present various identities and
computation formulas for certain classes of Apostol-type numbers and
polynomials. The results of this paper contain not only the
$\lambda$-Apostol-Daehee numbers and polynomials, but also Simsek numbers and
polynomials, the Stirling numbers of the first kind, the Daehee numbers, and
the Chu-Vandermonde identity. Furthermore, we derive an infinite series
representation for the $\lambda$-Apostol-Daehee polynomials. By using
functional equations containing the generating functions for the Cauchy numbers
and the Riemann integrals of the generating functions for the
$\lambda$-Apostol-Daehee numbers and polynomials, we also derive some
identities and formulas for these numbers and polynomials. Moreover, we give
implementation of a computation formula for the $\lambda$-Apostol-Daehee
polynomials in Mathematica by Wolfram language. By this implementation, we also
present some plots of these polynomials in order to investigate their behaviour
some randomly selected special cases of its parameters. Finally, we conclude
the paper with some comments and observations on our results.
