Difference between revisions of "First Chebyshev function"
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Revision as of 03:12, 29 April 2009
This article is about a function defined on positive reals (and in particular, natural numbers) obtained as the summatory function of an arithmetic function.
View other such summations
Definition
Let 
be a positive real number. The first Chebyshev function of , denoted 
or 
, is defined as:
,
where the sum is only over the prime numbers less than or equal to .
Relation with other counting functions
- Prime-counting function: Denoted
, this simply counts the number of primes less than or equal to .
- Second Chebyshev function: A similar summation, but this time of the von Mangoldt function over all prime powers less than or equal to .
