乗法的積分
∏ a b c d x = c b − a , {\displaystyle \prod _{a}^{b}{c^{dx}}=c^{b-a},} ∏ a b ( f ( x ) k ) d x = ( ∏ a b f ( x ) d x ) k , {\displaystyle \prod _{a}^{b}{(f(x)^{k})^{dx}}=(\prod _{a}^{b}{f(x)^{dx}})^{k},} ∏ a b ( c f ( x ) ) d x = c ∫ a b f ( x ) d x . {\displaystyle \prod _{a}^{b}{(c^{f(x)})^{dx}}=c^{\int _{a}^{b}\!f(x)dx}.}
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J. D. Dollard, C. N. Friedman, Product integrals and the Schrödinger Equation, Journ. Math. Phys. 18 #8,1598–1607 (1977).