Geodesic
A Regular Summability Method which Sums the Geometric Series to its Proper Value in the Whole Complex Plane
Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 179-188

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DOI

In this paper an explicit regular sequence-to-sequence summability method is presented which sums the geometric series to the value 1/(1-z) in all of C\{1} and to infinity at the point 1. The method also provides compact convergence in C \ [ 1, ∞) and therefore improves well-known results by Le Roy, Lindelöf and Mittag-Leffler.
DOI : 10.4153/CMB-1983-029-0
Mots-clés : 40G99 
Tomm, Ludwig. A Regular Summability Method which Sums the Geometric Series to its Proper Value in the Whole Complex Plane. Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 179-188. doi: 10.4153/CMB-1983-029-0
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     author = {Tomm, Ludwig},
     title = {A {Regular} {Summability} {Method} which {Sums} the {Geometric} {Series} to its {Proper} {Value} in the {Whole} {Complex} {Plane}},
     journal = {Canadian mathematical bulletin},
     pages = {179--188},
     year = {1983},
     volume = {26},
     number = {2},
     doi = {10.4153/CMB-1983-029-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-029-0/}
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