  In a recent paper Kachi and Tzermias give elementary proofs of four product
formulas involving zeta(3), pi, and Catalan's constant. They indicate that they
were not able to deduce these products directly from the values of a function
introduced in 1993 by Borwein and Dykshoorn. We provide here such a proof for
two of these formulas. We also give a direct proof for the other two formulas,
by using a generalization of the Borwein-Dykshoorn function due to Adamchik.
Finally we give an expression of the Borwein-Dykshoorn function in terms of the
"parameterized-Euler-constant function" introduced by Xia in 2013, which
happens to be a particular case of the "generalized Euler constant function"
introduced by K. and T. Hessami Pilehrood in 2010.
