Difference between revisions of "Fejér polynomial"
From Encyclopedia of Mathematics
Ulf Rehmann (talk | contribs) m (moved Fejer polynomial to Fejér polynomial over redirect: accented title) |
(TeX) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
| + | {{TEX|done}} | ||
A trigonometric polynomial of the form | A trigonometric polynomial of the form | ||
| − | + | $$\sum_{k=1}^n\frac1k(\cos(2n+k)x-\cos(2n-k)x),$$ | |
or a similar polynomial in sines. Fejér polynomials are used in constructing continuous functions for which their Fourier series have given singularities. | or a similar polynomial in sines. Fejér polynomials are used in constructing continuous functions for which their Fourier series have given singularities. | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> | + | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian) {{MR|0171116}} {{ZBL|0129.28002}} </TD></TR></table> |
Latest revision as of 15:11, 23 April 2014
A trigonometric polynomial of the form
$$\sum_{k=1}^n\frac1k(\cos(2n+k)x-\cos(2n-k)x),$$
or a similar polynomial in sines. Fejér polynomials are used in constructing continuous functions for which their Fourier series have given singularities.
References
| [1] | N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian) MR0171116 Zbl 0129.28002 |
How to Cite This Entry:
Fejér polynomial. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fej%C3%A9r_polynomial&oldid=23264
Fejér polynomial. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fej%C3%A9r_polynomial&oldid=23264
This article was adapted from an original article by S.A. Telyakovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article