Timeline for Computation involving Gauss integer function
Current License: CC BY-SA 4.0
2 events
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| Jun 5, 2022 at 22:39 | comment | added | Joe Silverman | The formula that Christophe Leuridan uses is more-or-less a special case of the average value relationship for the periodic Bernoulli polynomials, in this case applied to $\mathbb B_1(x)=x-\frac12$. In general, writing $B_n(x)$ for the $n$th Bernoulli polynomial and $\mathbb B_n(x)=B_n\bigl(x-\lfloor x\rfloor\bigr)$ for the version that is periodic modulo 1, we have: $$ \mathbb B_n(mx)= m^{n-1} \sum_{k=0}^{m-1} \mathbb B_n \left(x+\frac{k}{m}\right). $$ From this one can derive many similar formulas. | |
| May 6, 2022 at 20:19 | history | answered | Christophe Leuridan | CC BY-SA 4.0 |