Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.1

Infinite Products Arising in Paperfolding


Leyda Almodovar
Department of Mathematics
University of Iowa
Iowa City, IA 52242
USA

Victor H. Moll
Department of Mathematics
Tulane University
New Orleans, LA 70118
USA

Hadrian Quan
Department of Mathematics
UC Santa Cruz
Santa Cruz, CA 95064
USA

Fernando Roman
Department of Mathematics
Kansas State University
Manhattan, KS 66506
USA

Eric Rowland
Department of Mathematics
University of Liege
Belgium

Michole Washington
Department of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332
USA

Abstract:

J.-P. Allouche recently examined two infinite products where the term is a rational function of the index n raised to the term of the paperfolding sequence εn. A closed form is given only for one of them. We discuss an attempt to produce the missing closed form. We give a detailed analysis of convergence and a closed form for the analogous question, where the paperfolding sequence is replaced by a periodic one.

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(Concerned with sequence A034947.)

Received May 29 2015; revised version received April 21 2016. Published in Journal of Integer Sequences, May 11 2016.

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