The Generating Functions for Special Pringsheim Continued Fractions
Abstract
In previous works, some relations between Pringsheim continued fractions and vertices of the paths of minimal length on the suborbital graphs $\mathrm{\mathbf{F}}_{u,N}$ were investigated. Then, for special vertices, the relations between these vertices and Fibonacci numbers were examined. On the other hand, Koshy studied relation between recurrence relations of Fibonacci numbers, Pell numbers and generating functions. In this work, it is showed that every vertex on the path of minimal length of suborbital graph $\mathrm{\mathbf{F}}_{u,N}$ has a Pringsheim continued fraction. Then, by Koshy's motivation, the generating function of the recurrence relation of these pringsheim continued fractions are examined.
Keywords
Fibonacci Sequence, , Generating Functions, Pell Sequence, Continued Fractions, Suborbital Graphs
Thanks
The first author would like to thank the Scientific and Technological Research Council of Turkey (TUBITAK) for financial supports during her doctorate studies.
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