14 citations · 33 across the 30 of their papers we have counts for
5 papers · 1 filter
Gosper's and Ramanujan's infinite products and generalizations
Jean-Paul Allouche, John M. Campbell, Simon R. Holcombe +2
Gosper introduced many remarkable formulas involving infinite products. One such formula provides an evaluation of the product $$\prod_{n \geq 1} \frac{1}{e}\left(\frac{1}{3n} + 1\…
Doubling modulo odd integers, generalizations, and unexpected occurrences
Jean-Paul Allouche, Manon Stipulanti, Jia-Yan Yao
The starting point of this work is an equality between two quantities and found in the literature, which involve the {\em doubling-modulo-an-odd-integer} map, i.e., $x\in {…
Summing the sum of digits
Jean-Paul Allouche, Manon Stipulanti
We revisit and generalize inequalities for the summatory function of the sum of digits in a given integer base. We prove that several known results can be deduced from a theorem in…
An elementary proof of Bridy's theorem
Eric Rowland, Manon Stipulanti, Reem Yassawi
Christol's theorem states that a power series with coefficients in a finite field is algebraic if and only if its coefficient sequence is automatic. A natural question is how the s…
On digital sequences associated with Pascal's triangle
Pierre Mathonet, Michel Rigo, Manon Stipulanti +1
We consider the sequence of integers whose th term has base- expansion given by the th row of Pascal's triangle modulo (where is a prime number). We first present…