Summation of Rational Series Twisted by Strongly $B$-multiplicative Coefficients

[摘要] We evaluate in closed form series of the type $\sum u(n) R(n)$, with $(u(n))_n$ a strongly $B$-multiplicative sequence and $R(n)$ a (well-chosen) rational function. A typical example is:$$\sum_{n \geq 1} (-1)^{s_2(n)} \frac{4n+1}{2n(2n+1)(2n+2)} = -\frac{

[学科分类] 离散数学和组合数学

[关键词] Summation of series;Strongly $B$-multiplicative sequences;Paperfolding sequence;Shapiro-Rudin sequence.