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The Gibbs Phenomenon for [S, αn] Means and [T, αn] Means
Published online by Cambridge University Press: 20 November 2018
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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 cnk 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 
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- Copyright © Canadian Mathematical Society 1976
References
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