# Voronoi summation method

A matrix summation method of sequences. It is defined by a numerical sequence and denoted by the symbol . A sequence is summable by the method to a number if

In particular, if , , , the summability of a sequence by the -method to a number means that the sequence converges to . For , , one obtains the Cesàro summation method (cf. Cesàro summation methods). For , , , the -method is regular (cf. Regular summation methods) if and only if . Any two regular methods and are compatible (cf. Compatibility of summation methods).

The Voronoi summation method was first introduced by G.F. Voronoi [1] and was rediscovered by N.E. Nörlund in 1919. The method is therefore sometimes referred to in western literature as the Nörlund method and the symbol given to it is or .

#### References

[1] | G.F. [G.F. Voronoi] Woronoi, "Extension of the notion of the limit of the sum of terms of an infinite series" Ann. of Math. (2) , 33 (1932) pp. 422–428 ((With notes by J.D. Tamarkin.)) |

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

#### Comments

#### References

[a1] | C.N. Moore, "Summable series and convergence factors" , Dover, reprint (1966) |

**How to Cite This Entry:**

Voronoi summation method.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Voronoi_summation_method&oldid=18737