Multiple zeta sums via box splines (Q2710115)

The authors define box splines and prove six theorems based on them. They present a method for summing multiple series of the type NEWLINE\[NEWLINE\sum_{j \in Z^s}{1\over (a_{11}j_1+ \cdots+ a_{s1}j_s-x_1)^{2m_1} \cdots (a_{1n} j_1+ \cdots+ a_{sn}j_s -x_n)^{2m_n}}NEWLINE\]NEWLINE where the \(a_{ij}\) are integers and \(m_1,m_2, \dots,m_n\) are non-negative integers. The particular case \(s=n\) and the case \(x_1=x_2= x_3\cdots= x_n=0\) are studied in detail. At the end some examples are given.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00053].