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.
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© 2008 American Institute of Physics.
2008
American Institute of Physics
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