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On a family of infinite series with reciprocal Catalan numbers

We study a certain family of infinite series with reciprocal Catalan numbers. We first evaluate two special candidates of the family in closed form, where we also present some Catalan-Fibonacci relations. Then we focus on the general properties of the family and prove explicit formulas, including two types of integral representations.

preprint2022arXivOpen access
Kunle AdegokeRobert FrontczakTaras Goy
math.COmath.NT
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Kunle AdegokeRobert FrontczakTaras Goy

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