= Solution
The derivative fixed-point equation is unsuitable as an executable definition: requesting its first coefficient asks for the second coefficient of the same stream, then the third, indefinitely. It is not <productive>. As an algebraic equation it is also missing the constant coefficient: every scalar multiple of the <formal power series exponential>, including zero, satisfies it.
The integral equation gives the useful definition:
``
expx :: Fractional a => [a]
expx = plus one (integral expx)
``
The initial coefficient is available as `1 + 0`; each subsequent coefficient needs only a previously determined coefficient. The <recurrence relation> is $a_0=1$ and $a_{n+1}=a_n/(n+1)$, so \b[$a_n=1/n!$]. This proves both uniqueness of the formal solution and <productivity> of every finite coefficient <list prefix>.
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