不定和分
∑ x ψ ( x ) = ( x − 1 ) ψ ( x ) − x + C , {\displaystyle \sum _{x}\psi (x)=(x-1)\psi (x)-x+C,}
∑ x Γ ( x ) = ( − 1 ) x + 1 Γ ( x ) Γ ( 1 − x , − 1 ) e + C , {\displaystyle \sum _{x}\Gamma (x)=(-1)^{x+1}\Gamma (x){\frac {\Gamma (1-x,-1)}{e}}+C,} ただし、Γ(s,x) は不完全ガンマ函数.
∑ x ( x ) a = ( x ) a + 1 a + 1 + C , {\displaystyle \sum _{x}(x)_{a}={\frac {(x)_{a+1}}{a+1}}+C,} ただし、(x)a は下降階乗冪.
∑ x sexp a  ( x ) = ln a  ( sexp a  ( x ) ) ′ ( ln  a ) x + C . {\displaystyle \sum _{x}\operatorname {sexp} _{a}(x)=\ln _{a}{\frac {(\operatorname {sexp} _{a}(x))'}{(\ln a)^{x}}}+C.}
(ただし、sexp は超指数函数(英語版))