Exponential function: Difference between revisions

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Revision as of 07:06, 22 August 2025 edit Jacobolus (talk \| contribs) Extended confirmed users 40,092 edits m maybe better to link to the previous relevant section ← Previous edit		Latest revision as of 07:29, 22 August 2025 edit undo Jacobolus (talk \| contribs) Extended confirmed users 40,092 edits m →Complex exponential: use z instead of x
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Line 184: As with the real exponential function (see {{slink\|\|Functional equation}} above), the complex exponential satisfies the functional equation <math display=block>\exp(xz+yw)= \exp(xz)\cdot \exp(yw).</math> Among complex functions, it is the unique solution which is [[holomorphic]] at the point {{tmath\|1= xz = 0}} and takes the derivative {{tmath\|1}} there.<ref>{{cite book \|last=Hille \|first=Einar \|year=1959 \|title=Analytic Function Theory \|volume=1 \|place=Waltham, MA \|publisher=Blaisdell \|chapter=The exponential function \|at=§ 6.1, {{pgs\|138–143}} }}</ref> The [[complex logarithm]] is a [[left inverse function\|right-inverse function ]] of the complex exponential: