Geodesic
On the summation of certain iterated series
Journal of integer sequences, Tome 14 (2011) no. 6.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Furdui, Ovidiu and Trif, Tiberiu},
     title = {On the summation of certain iterated series},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
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     number = {6},
     year = {2011},
     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/