论文标题
多个涉及一般二阶数字序列的术语的总和
Multiple sums involving the terms of a general second order sequence of numbers
论文作者
论文摘要
我们评估嵌套的总和$ \ sum_ {a_ {n -1} = c}^{a_n} {\ sum_ {\ sum_ {a_ {n -2} = c} = c}^{a_ {a_ {n -1}}}}} { $ a_n $和$ c $是任何整数，$ x $是真实或复杂的变量。因此，我们评估了涉及一般二阶顺序的术语的多个总和，horadam序列$（w_j（a，b; p，q））$，该$定义为所有非阴性整数$ j $ y recurrence $ w_0 = a，w_0 = a，\，\，\，\，w_1 = b; 2）$;其中$ a $，$ b $，$ p $和$ q $是任意复数数字，$ p \ ne 0 $，$ q \ ne 0 $。
We evaluate the nested sum $\sum_{a_{n - 1} = c}^{a_n } {\sum_{a_{n - 2} = c}^{a_{n - 1} } { \cdots \sum_{a_0 = c}^{a_1 } {x^{a_0 } } } }$ where $a_n$ and $c$ are any integers and $x$ is a real or complex variable. Consequently, we evaluate multiple sums involving the terms of a general second order sequence, the Horadam sequence $(W_j(a,b;p,q))$, defined for all non-negative integers $j$ by the recurrence relation $W_0 = a,\,W_1 = b;\,W_j = pW_{j - 1} - qW_{j - 2}\, (j \ge 2)$; where $a$, $b$, $p$ and $q$ are arbitrary complex numbers, with $p\ne 0$, $q\ne 0$.
