On Integrals and Summable Trigonometric Series
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 433-440
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In considering a problem on certain summable (C, k) trigonometric series, R. D. James [13] used a symmetric pk+2- integral defined earlier to recapture the coefficients of the series from the sum function. James' formulas for the coefficients are more complicated than the usual Euler-Fourier form since the pk + 2 - integral is of order k + 2. It is shown that a generalized integral of order one for each non-negative integer k can be suitably defined to reduce James' formulas to the usual form.
Lee, Cheng-Ming. On Integrals and Summable Trigonometric Series. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 433-440. doi: 10.4153/CMB-1981-066-3
@article{10_4153_CMB_1981_066_3,
author = {Lee, Cheng-Ming},
title = {On {Integrals} and {Summable} {Trigonometric} {Series}},
journal = {Canadian mathematical bulletin},
pages = {433--440},
year = {1981},
volume = {24},
number = {4},
doi = {10.4153/CMB-1981-066-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-066-3/}
}
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