As The Limit of A Sequence
The number e is equal to the limit of several infinite sequences:
- and
- (both by Stirling's formula).
The symmetric limit,
may be obtained by manipulation of the basic limit definition of e. Another limit is
where is the nth prime and is the primorial of the nth prime.
where is the prime counting function. This definition is a direct corollary of the prime number theorem.
Also:
In the special case that, the result is the famous statement:
Read more about this topic: List Of Representations Of E
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