Geodesic
Note on the Strong Summability of Series
Glasgow mathematical journal, Tome 1 (1952) no. 1, pp. 16-20

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

Given the series ,the n-th Casáro sum of order k is defined by the relationwhere is the binomial coefficient . Let Then Σan is said to be summable (C; K) to the sum s if, as n → ∞, The series is said to be absolutely summable (C; k), or summable | is convergent. The series is said to be strongly summable (C; k) with index p, or summable [Ck, p], to the sum s ifIt is assumed that k and p are positive. 
Hyslop, J. M. Note on the Strong Summability of Series. Glasgow mathematical journal, Tome 1 (1952) no. 1, pp. 16-20. doi: 10.1017/S2040618500032883
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[page 16 note *] page 16 note * Kuttner, B., Journal London Math. Soc., 21 (1946), 118–122Google Scholar.

[page 17 note *] page 17 note * Winn, C. E., Math. Zeitschrift, 37 (1933), 481–492CrossRefGoogle Scholar.

[page 17 note †] page 17 note † it has been shown that, given any T-matrix, there is a series summable [C; 1, p], p < l, but not summable (T). See B. Kuttner, loc.cit.

[Page 17 note ‡] Page 17 note ‡ B. Kuttner, loc.cit.

[Page 18 note *] Page 18 note * See Hardy, Littlewood and Pólya, , Inequalities (Cambridge University Press, 1934), 229Google Scholar.

[Page 19 note *] Page 19 note * C. E. Winn, loc.cit.

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