Transformation formulas of finite sums into continued fractions
Daniel Duverney, Takeshi Kurosawa, Iekata Shiokawa
TL;DR
This paper introduces three general formulas that convert finite sums into continued fractions, expanding on previous work and providing new methods for representing sums as continued fractions.
Contribution
The paper presents novel transformation formulas that generalize existing expansions of finite sums into continued fractions.
Findings
Derived three general formulas for transforming sums into continued fractions
Generalized previous continued fraction expansions by Hone and Varona
Provided proofs and applications of the transformation formulas
Abstract
We state and prove three general formulas allowing to transform formal finite sums into formal continued fractions and apply them to generalize certain expansions in continued fractions given by Hone and Varona.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Mathematical Dynamics and Fractals