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2018 On the roots of the generalized Rogers-Ramanujan function
Pablo A. Panzone
Rocky Mountain J. Math. 48(8): 2653-2660 (2018). DOI: 10.1216/RMJ-2018-48-8-2653

Abstract

We give simple proofs of the fact that, for certain parameters, the roots of the generalized Rogers-Ramanujan function are irrational numbers and, for example, that at least one of the following two numbers is irrational: $ \{\sum _{n=1}^\infty {F_n }/({m^n \prod _{i=0}^{n-1}\phi (k+i)}), \sum _{n=1}^\infty {F_n }/(m^n \prod _{i=0}^{n-1}$ $\phi (k+i+1)) \}$, where $F_{n+2}=F_{n+1}+F_n$, $F_0=0,F_1=1$ (the Fibonacci sequence), $m$ is a natural number $> ({1+\sqrt 5})/{2}$ and $\phi (k)$ is any function taking positive integer values such that $\limsup _{k\rightarrow \infty } \phi (k)= \infty $.

Citation

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Pablo A. Panzone. "On the roots of the generalized Rogers-Ramanujan function." Rocky Mountain J. Math. 48 (8) 2653 - 2660, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2653

Information

Published: 2018
First available in Project Euclid: 30 December 2018

zbMATH: 06999278
MathSciNet: MR3894997
Digital Object Identifier: 10.1216/RMJ-2018-48-8-2653

Subjects:
Primary: 11J72, 11P84

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 8 • 2018
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