The inverse transform sum_(n = 1)^∞ (a_n x^n)/(n!) = ln(1 + sum_(n = 1)^∞ (b_n x^n)/(n!)) of the exponential transform 1 + sum_(n = 1)^∞ (b_n x^n)/(n!) = exp( sum_(n = 1)^∞ (a_n x^n)/(n!)) which relate sequences a_1, a_2, ... and b_1, b_2, ....
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