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On Cantor’s singular moments. (English) Zbl 0992.11054

The author uses Mellin transform techniques to answer a question posed by the problem Editor of the American Mathematical Monthly, namely, to compute \(J_{-1}=\sum_{n \geq 0}J_n\) where the \(J_n\) are Cantor’s singular moments defined by \[ J_n=\frac{2}{3(n+1)}\sum_{j=0}^n \binom{n+1}{j}\frac{B_j}{3.2^{j-1}-1} , \] where the \(B_n\) are Bernoulli numbers.

MSC:

11M41 Other Dirichlet series and zeta functions
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