First Chebyshev function
From Number
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 .
