Difference between revisions of "Trigonometric polynomial"
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''finite trigonometric sum'' | ''finite trigonometric sum'' | ||
An expression of the form | An expression of the form | ||
− | + | <table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t094/t094230/t0942301.png" /></td> </tr></table> | |
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− | with real coefficients | + | with real coefficients <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t094/t094230/t0942302.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t094/t094230/t0942303.png" />; the number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t094/t094230/t0942304.png" /> is called the order of the trigonometric polynomial (provided <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t094/t094230/t0942305.png" />). A trigonometric polynomial can be written in complex form: |
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− | the number | ||
− | is called the order of the trigonometric polynomial (provided | ||
− | A trigonometric polynomial can be written in complex form: | ||
− | + | <table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t094/t094230/t0942306.png" /></td> </tr></table> | |
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where | where | ||
− | + | <table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t094/t094230/t0942307.png" /></td> </tr></table> | |
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Trigonometric polynomials are an important tool in the [[Approximation of functions|approximation of functions]]. | Trigonometric polynomials are an important tool in the [[Approximation of functions|approximation of functions]]. | ||
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====Comments==== | ====Comments==== | ||
Cf. also [[Trigonometric series|Trigonometric series]]. | Cf. also [[Trigonometric series|Trigonometric series]]. |
Revision as of 14:53, 7 June 2020
finite trigonometric sum
An expression of the form
![]() |
with real coefficients ,
; the number
is called the order of the trigonometric polynomial (provided
). A trigonometric polynomial can be written in complex form:
![]() |
where
![]() |
Trigonometric polynomials are an important tool in the approximation of functions.
Comments
Cf. also Trigonometric series.
How to Cite This Entry:
Trigonometric polynomial. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Trigonometric_polynomial&oldid=49036
Trigonometric polynomial. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Trigonometric_polynomial&oldid=49036
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article