https://en.formulasearchengine.com/index.php?title=Talk:Trigonometric_polynomial&feed=atom&action=historyTalk:Trigonometric polynomial - Revision history2020-10-28T02:51:10ZRevision history for this page on the wikiMediaWiki 1.36.0-alphahttps://en.formulasearchengine.com/index.php?title=Talk:Trigonometric_polynomial&diff=296250&oldid=preven>Waldir: copyedit2014-02-20T03:39:29Z<p>copyedit</p>
<p><b>New page</b></p><div>{{maths rating|class=start|importance=low|field=analysis}}<br />
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== Error in formula ==<br />
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It seems to me there's something wrong with this line for the real trig polynomial:<br />
:<math>T_N(x) = \sum_{n=0}^N a_n \cos (nx) + \sum_{n=0}^N a_n \sin(nx) \qquad (x \in \mathbf{R})</math><br />
Shouldn't the coefficients for cos and sin be different, like <math>a_n \cos (nx)</math> and <math>b_n \sin (nx)</math>? Because, otherwise wouldn't this just be a single sum like this:<br />
:<math>T_N(x) = \sum_{n=0}^N {a_n (\cos (nx) + \sin(nx))}</math><br />
Something is definitely wrong here...<br/><br />
[[User:Edsanville|Edsanville]] 20:32, 23 Aug 2004 (UTC)<br />
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: You were correct, i fixed the definition. My mistake. [[User:MathMartin|MathMartin]] 11:45, 27 Aug 2004 (UTC)<br />
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== Notational inconsistency ==<br />
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The page uses an upright "i" for ''i'', but inconsistently uses italic ''e'' for ''e''. I prefer ''i'' for the imaginary unit in most cases, but I didn't change the page because I don't want to step on toes. [[User:165.189.91.148|165.189.91.148]] 18:51, 1 June 2006 (UTC)<br />
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== Confusing Notes. ==<br />
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I am confused what the following two lines are trying to say:<br />
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Using the relation <br />
:<math>T(x) = \mathrm{e}^{\mathrm{i}Nx} t(x) \,\!</math><br />
we can construct a [[bijective]] mapping between the ''complex trigonometric polynomials'' and the ''real trigonometric polynomials''. Thus a trigonometric polynomial can be considered a periodic function on the [[real line]], with period some multiple of 2π, or as a function on the [[unit circle]].<br />
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First the relation above, while certainly bijective, does not directly give a bijection between real and complex trigonometric polynomails. Also, the second sentence doesn't need the first, so it shouldn't start with "Thus".<br />
[[User:Thenub314|Thenub314]] ([[User talk:Thenub314|talk]]) 18:39, 9 September 2008 (UTC)<br />
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: I'm also confused. The second sentence is probably what is meant, and I guess the first sentence is an explanation which I don't quite understand. Those two lines do need to be rewritten. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 03:03, 10 September 2008 (UTC)<br />
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== Real case special case of complex? ==<br />
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I'm trying to see if the two separate definitions given in this article are "compatible". That is, I think we should be able to have any real trigonometric polynomial by setting the right coefficients in the general complex case, but the way the complex polynomials are defined doesn't seem to let me. If I set al the coefficients in front of the "i" in the general definitions, I will be forced to match the coefficients for cos(nx) with those of the real polynomial, leaving the sin terms unmatched. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/190.118.32.209|190.118.32.209]] ([[User talk:190.118.32.209|talk]]) 03:48, 25 April 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot--><br />
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: Just passing by, it seems to me that you don't need the i in front of b_n sin(nx) for the complex part. cf Rudin Principles of Mathematical Analysis p 186 <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/39.120.161.171|39.120.161.171]] ([[User talk:39.120.161.171|talk]]) 04:03, 9 July 2013 (UTC)</span><!-- Template:Unsigned IP --></div>en>Waldir