Like the constant HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi></math> ht , Apéry's constant plays an important role in mathematics as well as in physics (see [[9]]). Like HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi></math> ht , Apéry's constant appears unexpectedly in quite a number of mathematical results.