On Product (E, 1) (C, α, ) Summabilityof Fourier Series and its Conjugate Series

  • Suyash Narayan Mishra Department of Applied Sciences, Institute of Engineering and Technology, Lucknow (U.P.)
  • Amrita Tripathi Department of Applied Sciences, Amity School of Applied Sciences, Amity University, Lucknow
Keywords: (E, 1) means, (C, α) means, (E, 1) (C, α, β) product Means, Fourier series, Conjugate Series. AMS Mathematics Subject Classification: 42B05, 42B08.

Abstract

Summability is defined as a division of mathematical analysis where in an infinite series which is divergent by conventional summation methods is made to converge to a sum say‘w’ & become summable through dissimilar summation methods. Ernesto Cesaro gave one such method known as C Method in which (C, 1) is the notation for ordinary Cesaro summation & (C, α) is the notation for generalized Cesaro summation. Euler provided summation formula which sums infinite series called (E, 1) summation method. Generalized (E, 1) (C, 1) to (E, 1) (C, α) (α > 0) product summation is given by S.N.Mishra & Harsh Joshi [7]. The objective of this paper is to generalize (E, 1)(C, α) (α > 0) to (E, 1)(C, α , β) (α > 0)( β > -1) so that the series which can’t be made summable by (E, 1)(C, 1) & (E, 1)(C, α) methods can be made summable by (E, 1)(C, α , β) (α > 0)( β > -1)methods

Published
2021-12-31
Issue
Vol 35 No 01 (2021): JOURNAL OF NATIONAL ACADEMY OF MATHEMATICS INDIA
Section
Articles

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