A Symmetric Approximate Perron Integral for the Coefficient Problem of Convergent Trigonometric Series

1990 ◽  
Vol 16 (1) ◽  
pp. 329 ◽  
Author(s):  
Lee
Keyword(s):  
Trigonometric Series ◽  
Coefficient Problem ◽  
Convergent Trigonometric Series ◽  
Perron Integral

The Representation of (C, k) Summable Series in Fourier Form

1978 ◽  
Vol 21 (2) ◽  
pp. 149-158 ◽  
Author(s):  
G. E. Cross
Keyword(s):  
Trigonometric Series ◽  
Point Of View ◽  
Perron Integral ◽  
Image Position

Several non-absolutely convergent integrals have been defined which generalize the Perron integral. The most significant of these integrals from the point of view of application to trigonometric series are the Pn- and pn-integrals of R. D. James [10] and [11]. The theorems relating the Pn -integral to trigonometric series state essentially that if the series1.1

On the K-dependence of the electrical field in a crystalline slab of oscillating charges

1981 ◽  
Vol 59 (7) ◽  
pp. 929-933 ◽  
Author(s):  
J. Grindlay
Keyword(s):  
Electric Field ◽  
Trigonometric Series ◽  
Wave Vector ◽  
Short Range ◽  
Electrical Field ◽  
Ewald Sum ◽  
Convergent Trigonometric Series ◽  
Short Range Part ◽  
Range Part

The short range part of the electric field of a crystalline slab array of oscillating charges (a) is related to the Ewald sum and (b) can be represented by a rapidly convergent trigonometric series involving the wave vector K. Values for the coefficients of the first few terms of this series are reported for lattice sites in the sc, fcc, bcc, NaCl, CsCl structures and the symmetry directions (1,0,0), (1,1,0), (1,1,1).

Uniqueness of Rectangularly Convergent Trigonometric Series

1993 ◽  
Vol 137 (1) ◽  
pp. 145 ◽  
Author(s):  
J. Marshall Ash ◽  
Chris Freiling ◽  
Dan Rinne
Keyword(s):  
Trigonometric Series ◽  
Convergent Trigonometric Series
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