乗法的不定和分
∏ x Γ ( x ) = C Γ ( x ) x − 1 K  ( x ) = C Γ ( x ) x − 1 e z 2 ln  ( 2 π ) − z 2 − z 2 − ψ ( − 2 ) ( z ) = C G  ( x ) , {\displaystyle \prod _{x}\Gamma (x)={\frac {C\Gamma (x)^{x-1}}{\operatorname {\mathit {K}} (x)}}=C\Gamma (x)^{x-1}e^{{\frac {z}{2}}\ln(2\pi )-{\frac {z^{2}-z}{2}}-\psi ^{(-2)}(z)}=C\operatorname {\mathit {G}} (x),} (ただし、G(x) はバーンズのG函数である)
∏ x sexp a  ( x ) = C ( sexp a  ( x ) ) ′ sexp a  ( x ) ( ln  a ) x . {\displaystyle \prod _{x}\operatorname {sexp} _{a}(x)={\frac {C(\operatorname {sexp} _{a}(x))'}{\operatorname {sexp} _{a}(x)(\ln a)^{x}}}.} (ただし、sexp は超指数函数である)