${\displaystyle a\in (\dots ,-2,-1,0,1,2,\dots )}$
${\displaystyle b\in (\dots ,-2,-1,0,1,2,\dots )}$
${\displaystyle n=b-a+1}$

${\displaystyle k\in \{a,a+1,\dots ,b-1,b\}}$

${\displaystyle {\begin{matrix}{\frac {1}{n}}&{\mbox{dla }}a\leqslant k\leqslant b,\ k\in {\mathbb {Z} }\\0&{\mbox{w przeciwnym wypadku}}\end{matrix}}}$

${\displaystyle {\begin{matrix}0&{\mbox{dla }}k<a\\{\frac {\lfloor k\rfloor -a+1}{n}}&{\mbox{dla }}a\leqslant k\leqslant b\\1&{\mbox{dla }}k>b\end{matrix}}}$

${\displaystyle {\frac {a+b}{2}}}$

${\displaystyle {\frac {a+b}{2}}}$

N/A

${\displaystyle {\frac {n^{2}-1}{12}}}$

${\displaystyle 0}$

${\displaystyle -{\frac {6(n^{2}+1)}{5(n^{2}-1)}}}$

${\displaystyle \ln(n)}$

${\displaystyle {\frac {e^{at}-e^{(b+1)t}}{n(1-e^{t})}}}$

${\displaystyle {\frac {e^{iat}-e^{i(b+1)t}}{n(1-e^{it})}}}$