Geodesic
The Gibbs Phenomenon for [S, αn] Means and [T, αn ] Means
Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 209-211

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The Gibbs phenomenon of the Fourier series for different summability methods has been investigated by various authors. In this note, we study the same for the [S, αn ] method of summability introduced by Meir and Sharma [3]. The corresponding result for the [T, αn ] method of summability due to Powell [5] can be worked out in exactly the same way.The elements c nk of the [S, αn ] matrix are defined by the relations: 1 where 0<αn <1. The [S, αn ] matrix is regular if and only if 
Swaminathan, V. The Gibbs Phenomenon for [S, αn] Means and [T, αn ] Means. Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 209-211. doi: 10.4153/CMB-1976-032-8
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[1] 1. Ishiguro, K., Zur Gibbschen Erscheinung für das Kreisverfahren. Math. Z. 76, 288-294 (1961). Google Scholar

[2] 2. Ishiguro, K., Über das Sα-Verfahren bei Fourier-Reihen. Math. Z. 80, 4–11 (1962).10.1007/BF01162364 Google Scholar | DOI

[3] 3. Meir, A. and Sharma, A., A generalization of the Sa-summation method. Proc. Camb. Phil. Soc. 67, 61–66 (1970).10.1017/S0305004100057091 Google Scholar | DOI

[4] 4. Miracle, C. L., The Gibbs phenomenon for Taylor means and for [F, d] means. Can. J. Math. 12, 660–673 (1960).10.4153/CJM-1960-059-2 Google Scholar | DOI

[5] 5. Powell, R. E., The T(r) summability transform. J. Analyse Math. 20, 289–304 (1967).10.1007/BF02786677 Google Scholar | DOI

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