We describe a general method to construct a sequence {c(n)} not equivalent to 0 whose discrete moments satisfy Sigma(infinity)(n=1) n(k) c(n) = 0 for all values k = 0, 1, 2, ... of the exponent. We focus on a specific example, but a vast set of analogous constructions is possible.
Fontana, L., Laeng, E. (2022). A Nonzero Sequence All of Whose Discrete Moments Are Equal to Zero. THE AMERICAN MATHEMATICAL MONTHLY, 129(7), 681-684 [10.1080/00029890.2022.2071570].
A Nonzero Sequence All of Whose Discrete Moments Are Equal to Zero
Fontana, L;
2022
Abstract
We describe a general method to construct a sequence {c(n)} not equivalent to 0 whose discrete moments satisfy Sigma(infinity)(n=1) n(k) c(n) = 0 for all values k = 0, 1, 2, ... of the exponent. We focus on a specific example, but a vast set of analogous constructions is possible.
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