E (broj)

Ovaj članak ili neki od njegovih odlomaka nije dovoljno potkrijepljen izvorima (literatura, veb-sajtovi ili drugi izvori). Ako se pravilno ne potkrijepe pouzdanim izvorima, sporne rečenice i navodi mogli bi biti izbrisani. Pomozite Wikipediji tako što ćete navesti validne izvore putem referenci te nakon toga možete ukloniti ovaj šablon.

Broj e zove se još Eulerov (fon. Ојlerov) broj ili Napierova konstanta je baza prirodnog logaritma. U sadašnjoj matematici jedan je od značajnijih brojeva. U tu grupu spadaju još 0 (broj), 1 (broj), pi (π) i imaginarna jedinica (i).

Eulerov broj broj je iracionalan i transcedentalan broj. On iznosi

e ≈ 2,71828 18284 59045 23536 02874 71352 ...

Definicija

Broj e je

Granična vrijednost beskonačnog niza
$e=\lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}$
Zbir beskonačnog niza :
$e=\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1!}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+\cdots$
Gdje je n! faktorijel n.
Pozitivna vrijednost koja zadovoljava
$\int _{1}^{e}{\frac {1}{t}}\,dt={1}$

Ekvivalencija između ova tri iskaza može se dokazati.
Susreće se i kao dio eulerovog identiteta:
$e^{\mathrm {i} \cdot \pi }=-1$

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