不定和分
∑ x cot  a x = − i x − i ψ e 2 i a ( x ) a + C ( a ≠ n π 2 ) , {\displaystyle \sum _{x}\cot ax=-ix-{\frac {i\psi _{e^{2ia}}(x)}{a}}+C\quad (a\neq {\frac {n\pi }{2}}),}
∑ x artanh a x = 1 2 ln  ( ( − 1 ) x Γ ( − 1 a ) Γ ( x + 1 a ) Γ ( 1 a ) Γ ( x − 1 a ) ) + C , {\displaystyle \sum _{x}\operatorname {artanh} \,ax={\frac {1}{2}}\ln \left({\frac {(-1)^{x}\Gamma \left(-{\frac {1}{a}}\right)\Gamma \left(x+{\frac {1}{a}}\right)}{\Gamma \left({\frac {1}{a}}\right)\Gamma \left(x-{\frac {1}{a}}\right)}}\right)+C,}
∑ x arctan  a x = i 2 ln  ( ( − 1 ) x Γ ( − i a ) Γ ( x + i a ) Γ ( i a ) Γ ( x − i a ) ) + C . {\displaystyle \sum _{x}\arctan ax={\frac {i}{2}}\ln \left({\frac {(-1)^{x}\Gamma ({\frac {-i}{a}})\Gamma (x+{\frac {i}{a}})}{\Gamma ({\frac {i}{a}})\Gamma (x-{\frac {i}{a}})}}\right)+C.}