For \({\sl {s}}:=(s_1,\ldots ,s_r)\in \mathbb {N}^r\)  and \(s_1>1\) , the Kaneko-Tsumura multiple \(T\) -values (MTVs) are defined by (see [1]}, [2]})
\(T({\sl {s}})&\equiv T(s_1,\ldots ,s_r):=2^r\displaystyle \sum _{n_1>\cdots >n_r>0\atop n_i\equiv r-i+1\ (\text{mod}\ 2)} \displaystyle \frac{1}{n_1^{s_1}\cdots n_r^{s_r}}\\&=2^r\displaystyle \sum _{n_1>\cdots >n_r>0} \displaystyle \frac{1}{(2n_1-r)^{s_1}\cdots (2n_r-1)^{s_r}}\in \mathbb {R}.\) 

Для \({\sl {s}}:=(s_1,\ldots ,s_r)\in \mathbb {N}^r\)  и \(s_1>1\) , множественные значения Канеко-Цумуры (MTV) определяются как (см. [1]}, [2]})

\(T({\sl {s}})&\equiv T(s_1,\ldots ,s_r):=2^r\displaystyle \sum _{n_1>\cdots >n_r>0\atop n_i\equiv r-i+1\ (\text{mod}\ 2)} \displaystyle \frac{1}{n_1^{s_1}\cdots n_r^{s_r}}\\&=2^r\displaystyle \sum _{n_1>\cdots >n_r>0} \displaystyle \frac{1}{(2n_1-r)^{s_1}\cdots (2n_r-1)^{s_r}}\in \mathbb {R}.\)