摘要

In a recent paper Kachi and Tzermias give elementary proofs of four product formulas involving , , 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, 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. Hessami Pilehrood and T. Hessami Pilehrood in 2010.

  • 出版日期2015-5

全文