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Constante van Gelfond

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Het getal , oftewel e tot de macht , wordt de constante van Gelfond genoemd. De numerieke waarde bedraagt bij benadering 23,1406926...

De constante kan ook geschreven worden als:


waarin de imaginaire eenheid is.

Definieert men

en voor


dan convergeert[1]

snel naar .


Het getal is een transcendent getal. Dit werd aangetoond door Aleksander Gelfond aan de hand van de stelling van Gelfond-Schneider.

Het is opmerkelijk dat van andere combinaties van e en zoals , of (nog) niet bekend is of die transcendent of zelfs maar irrationaal zijn.

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Constante van Gelfond
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