Difference between revisions of "First Chebyshev function"

From Number
Jump to: navigation, search
(Created page with '{{counting function}} ==Definition== Let <math>x</math> be a positive real number. The '''first Chebyshev function''' of <math>x</math>, denoted <math>\vartheta(x)</math> or <m...')
 
Line 1: Line 1:
{{counting function}}
+
{{till-now summation}}
  
 
==Definition==
 
==Definition==

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