Geodesic
On the summation of certain iterated series
Journal of integer sequences, Tome 14 (2011) no. 6
The paper gives a unified treatment of the summation of certain iterated series of the form $ \sum_{n=1}^{\infty}\sum_{m=1}^{\infty}a_{n+m},$ where $ (a_{n})_{n\in \mathbb{N}}$ is a sequence of real numbers. We prove that, under certain conditions, the double iterated series equals the difference of two single series.
Classification : 40A05, 40B05
Keywords: Bell numbers, iterated series, double alternating harmonic series, Stirling numbers, wolstenholme series 
@article{JIS_2011__14_6_a2,
     author = {Furdui,  Ovidiu and Trif,  Tiberiu},
     title = {On the summation of certain iterated series},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {6},
     zbl = {1235.40004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_6_a2/}
}
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Furdui,  Ovidiu; Trif,  Tiberiu. On the summation of certain iterated series. Journal of integer sequences, Tome 14 (2011) no. 6. http://geodesic.mathdoc.fr/item/JIS_2011__14_6_a2/