Content deleted Content added
Line 18:
==Values==
The Fabius function is constant zero for all non-positive arguments, and assumes rational values at non-negative [[dyadic rational]] arguments. These values are given by the following formula:
:<math>
f\left(\frac n{2^m}\right)=\frac{1}{2}-\frac1{2^{m^2+1}\,\left(\frac{1}{2};\frac{1}{2}\right)_m}\,\sum_{k=0}^m\,\frac{\left[\begin{smallmatrix}m\\[3pt] k\end{smallmatrix}\right]_{1/2}}{2^{k\,(k-1)}\,(m+k)!}\sum^{2^{m+k}-1}_{j=0}(-1)^{s_2(j)}\,\left(j-2^k\,n+\tfrac{1}{2}\right)^{m+k}\sgn\left(j-2^k\,n+\tfrac{1}{2}\right),</math>
| |||