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

Для \({\sl {s}}:=(s_1,\ldots ,s_r)\in \mathbb {N}^r\) и \(s_1>1\), мы определили в [1] множественные значения \(S\) (MSV) по следующей формуле:

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