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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Roy, Le, Annales de la Faculté des sciences de Toulouse (2), 2 (1900), 317–430 (323). Google Scholar

[2] 2. Lindelöf, , Journal de mathématiques (5), 9 (1903), 213–21. Google Scholar

[3] 3. Mittag-Leffler, , Atti del IV congressi Internaz. i. 67–85; Rome 1908. Google Scholar

[4] 4. Tomm, L., Über die Summierbarkeit der geometrischen Reihe mit regulären Verfahren; author's dissertation; Ulm, West Germany. Google Scholar

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