On the gauss trigonometric sum

2000 ◽  
Vol 68 (2) ◽  
pp. 154-158
Author(s):  
M. Z. Garaev
Keyword(s):  
Trigonometric Sum

scholarly journals Lacunary trigonometric sum and probability

1970 ◽  
Vol 22 (4) ◽  
pp. 502-510 ◽  
Author(s):  
Shigeru Takahashi
Keyword(s):  
Trigonometric Sum

Sharing Teaching Ideas: Cos_x + Sin_x and the Trigonometric Sum and Difference Identities

2002 ◽  
Vol 95 (7) ◽  
pp. 510-514
Keyword(s):  
Formal Proofs ◽  
Trigonometric Sum ◽  
Teaching Ideas

That the cosine or sine of a sum or difference is not the sum or difference of the cosines or sines is easy to establish by counterexample. However, the actual expansions for cos (A ± B) and sin (A ± B) are not intuitively obvious for most students. Standard textbooks do cover the derivations of these expansions, but the results have a greater impact if students conjecture them first. This article describes a lesson that introduces the formal proofs of the trigonometric sum and difference identities. In this activity, students discover the expansions for the cosine and sine of a sum and difference by using technology to generate selected graphs and by analyzing patterns in these graphs. The only prerequisite is the ability to find the equation of a sinusoid when the graph of the function is given.

Shorter Notes: On a Positive Trigonometric Sum

1968 ◽  
Vol 19 (6) ◽  
pp. 1507
Author(s):  
Richard Askey ◽  
James Fitch ◽  
George Gasper
Keyword(s):  
Trigonometric Sum

scholarly journals On a trigonometric sum of Vinogradov

2004 ◽  
Vol 105 (2) ◽  
pp. 251-261 ◽  
Author(s):  
Horst Alzer ◽  
Stamatis Koumandos
Keyword(s):  
Trigonometric Sum

Simple trigonometric models for narrow-band stationary processes

1982 ◽  
Vol 19 (A) ◽  
pp. 333-343
Author(s):  
A. M. Hasofer
Keyword(s):  
Stationary Process ◽  
Finite Interval ◽  
Narrow Band ◽  
Stationary Processes ◽  
Gaussian Stationary Process ◽  
Trigonometric Sum

Over a finite interval, a Gaussian stationary process can be approximated by a finite trigonometric sum, and the error introduced by the approximation can be exactly bounded, as far as the distribution of the upper tail of the maximum is concerned. A simple case is exhibited, where a narrow band process is well approximated by means of a two-term trigonometric representation.

A Sharp Inequality for a Trigonometric Sum

2012 ◽  
Vol 10 (1) ◽  
pp. 313-320
Author(s):  
Horst Alzer ◽  
Stamatis Koumandos
Keyword(s):  
Sharp Inequality ◽  
Trigonometric Sum

scholarly journals Application of Mathematical Theories of Approximation to Aerial Smoothing in Radio Astronomy

1957 ◽  
Vol 10 (1) ◽  
pp. 16 ◽  
Author(s):  
J Arsac
Keyword(s):  
Systematic Error ◽  
Finite Length ◽  
Radio Astronomy ◽  
Brightness Distribution ◽  
Radio Brightness ◽  
Object Function ◽  
Trigonometric Sum ◽  
Radio Brightness Distribution ◽  
Image Function ◽  
The Difference

An aerial rarely provides a perfect image of a radio brightness distribution. If we consider an array as a filter of "spatial harmonics", the image function is a trigonometric sum approximating the object function. An application of mathematical theories shows the influence of the length and the shape of the array on the difference between object and image. Whatever the array, the image contrasts are bounded. The results provided by various arrays of the same length may be reduced by linear transforms. Inaccuracies of measurement, especially those due to the receiver noise, add to the systematic error due to the finite length of the antenna. We may try to get a compromise between these various causes of uncertainty.

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