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  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 .
|||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.))|
|||G.H. Hardy, "Divergent series" , Clarendon Press (1949)|
|[a1]||C.N. Moore, "Summable series and convergence factors" , Dover, reprint (1966)|
Voronoi summation method. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Voronoi_summation_method&oldid=18737