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On Integrals and Summable Trigonometric Series

Published online by Cambridge University Press:  20 November 2018

Cheng-Ming Lee
Cheng-Ming Lee*
Affiliation:
University of Wisconsin-Milwaukee Milwaukee, Wisconsin 53201
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Abstract

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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 433 - 440
Copyright
Copyright © Canadian Mathematical Society 1981

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