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In mathematics, the Chebyshev function is either of two related functions. The first Chebyshev function ϑ(x) or θ(x) is given by where denotes the natural logarithm, with the sum extending over all prime numbers p that are less than or equal to x. The second Chebyshev function ψ(x) is defined similarly, with the sum extending over all prime powers not exceeding x Both functions are named in honour of Pafnuty Chebyshev.

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rdfs:label	Chebyshev function (en)
rdfs:comment	In mathematics, the Chebyshev function is either of two related functions. The first Chebyshev function ϑ(x) or θ(x) is given by where denotes the natural logarithm, with the sum extending over all prime numbers p that are less than or equal to x. The second Chebyshev function ψ(x) is defined similarly, with the sum extending over all prime powers not exceeding x Both functions are named in honour of Pafnuty Chebyshev. (en)
sameAs	Chebyshev function Chebyshev function
dbp:wikiPageUsesTemplate	dbt:= dbt:Arxiv dbt:Citation_needed dbt:Math dbt:Mathworld dbt:Mvar dbt:Note dbt:OEIS2C dbt:Ref dbt:Sfrac dbt:Sqrt dbt:Isbn dbt:Abs dbt:Apostol_IANT dbt:Planetmathref
Subject	Arithmetic functions
Link from a Wikipage to an external page	http://www.math.ucsb.edu/~stopple/explicit.html https://books.google.com/books%3Fvid=ISBN0387950974&id=U91lsCaJJmsC&pg=PA104&lpg=PA104
thumbnail	wiki-commons:Special:FilePath/ChebyshevPsi.png?width=300
foaf:depiction
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Chebyshev_function?oldid=1061805369&ns=0
Wikipage page ID	5793598 (xsd:integer)
page length (characters) of wiki page	12117 (xsd:nonNegativeInteger)
Wikipage revision ID	1061805369 (xsd:integer)
Link from a Wikipage to another Wikipage	Logarithm Alain Connes Big O notation Statistical mechanics Taylor series Von Mangoldt function Arithmetic functions Pafnuty Chebyshev Pierre Dusart Zeros and poles Prime-counting function Prime number Prime number theorem Primorial John Edensor Littlewood Erhard Schmidt G. H. Hardy Explicit formulae for L-functions Hans Carl Friedrich von Mangoldt Harold Davenport Least common multiple Mathematics Natural logarithm Riemann hypothesis Riemann zeta function
has abstract	In mathematics, the Chebyshev function is either of two related functions. The first Chebyshev function ϑ(x) or θ(x) is given by where denotes the natural logarithm, with the sum extending over all prime numbers p that are less than or equal to x. The second Chebyshev function ψ(x) is defined similarly, with the sum extending over all prime powers not exceeding x where Λ is the von Mangoldt function. The Chebyshev functions, especially the second one ψ(x), are often used in proofs related to prime numbers, because it is typically simpler to work with them than with the prime-counting function, π(x) (See , below.) Both Chebyshev functions are asymptotic to x, a statement equivalent to the prime number theorem. Both functions are named in honour of Pafnuty Chebyshev. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Chebyshev_function
is Wikipage redirect of	Chebyshev's function Chebyshev functions Mangoldt summatory function Von Mangoldt summatory function Tchebysheff function Tchebyshev function
is Link from a Wikipage to another Wikipage of	Greek letters used in mathematics, science, and engineering List of things named after Pafnuty Chebyshev Arithmetic function Bertrand's postulate Mertens function Chebyshev (disambiguation) List of mathematical functions List of Russian mathematicians List of Russian people List of Russian scientists Explicit formulae for L-functions Farey sequence Lowell Schoenfeld Chebyshev's function Chebyshev functions Least common multiple Mangoldt summatory function
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Chebyshev_function

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