Ramanujan summation of divergent series
Candelpergher, B
HAL, hal-01150208 / Harvested from HAL
In Chapter VI of his second Notebook Ramanujan introduce the Euler-MacLaurin formula to define the " constant " of a series. When the series is divergent he uses this " constant " like a sum of the series. We give a rigorous definition of Ramanujan summation and some properties and applications of it. These properties of the summation seems very unusual so in the last chapter we give a general algebraic view on summation of series that unify Ramanujan summation with the classical summations procedures.
Publié le : 2017-03-29
Classification:  Ramanujan summation,  [MATH]Mathematics [math],  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]
@article{hal-01150208,
     author = {Candelpergher, B},
     title = {Ramanujan summation of divergent series},
     journal = {HAL},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01150208}
}
Candelpergher, B. Ramanujan summation of divergent series. HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01150208/