# De la Vallée-Poussin singular integral

From Encyclopedia of Mathematics

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An integral of the form

(see also de la Vallée-Poussin summation method). The sequence converges uniformly to for functions which are continuous and -periodic on [1]. If

at a point , then as . The following equality is valid [2]:

#### References

[1] | G.H. Hardy, "Divergent series" , Clarendon Press (1949) |

[2] | I.P. Natanson, "Constructive function theory" , 1 , F. Ungar (1964) (Translated from Russian) |

#### Comments

The notation stands for ( terms), and (also terms). Thus,

**How to Cite This Entry:**

De la Vallée-Poussin singular integral.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=De_la_Vall%C3%A9e-Poussin_singular_integral&oldid=33425

This article was adapted from an original article by P.P. Korovkin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article