Automatic Conjecturing and Proving of Exact Values of Some Infinite Families of Infinite Continued Fractions

By Robert Dougherty-Bliss and Doron Zeilberger

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Appeared in the Ramanujan Journal v. 61, no. 1, (2023), 31-47.

    In fond memory of Richard A. Askey (1933-2019), that taught us that Special Functions are Useful Functions

First Version: March 31, 2020 . This version: May 20, 2020.

We are sure that Richard Askey would have appreciated this paper, since it is yet another example how Special Functions, combined with symbolic computation, could lead to interesting new results.

Acknowledgment: The authors would like to thank the OEIS for its help in identifying promising sequences of integers that arose in the evaluation of these continued fractions, as well as Alex Kontorovich who forwarded us some very useful feedback on an earlier version from a very distinguished and esteemed number theorist (not to be confused with his equally brilliant brother), who out of natural modesty, asked not to be named, and we reluctantly agreed to keep him anonymous.

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