On series involving Fibonacci and Lucas numbers I
On series involving Fibonacci and Lucas numbers I
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关于斐波那契数列和卢卡斯数列 I
DOI：
10.1063/1.2841912
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
I. Shiokawa
中科院分区：
文献类型：
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作者：
D. Duverney;I. Shiokawa
我们使用经典函数，如 theta 函数、第一类和第二类完全椭圆积分、朗伯级数和 q 指数函数，对斐波那契数和卢卡斯数的各种倒数和的闭式求值和表达式的结果进行总结和分类。在最后一节中，我们给出有理函数序列的闭合形式表达式，并评估涉及斐波那契数和卢卡斯数的序列。
We summarize and classify results on the evaluations and expressions in closed from of various reciprocal sums of Fibonacci numbers and Lucas numbers using classical functions, such as theta functions, complete elliptic integrals of the first and second kind, Lambert series, and q‐exponential functions. In the final section we give closed form expressions of series of rational functions and evaluate series involving Fibonacci and Lucas numbers.