Mathematics > Classical Analysis and ODEs
[Submitted on 21 Sep 2013]
Title:More Jordan type inequalities
View PDFAbstract:The function $ \tan(\pi x / 2) / (\pi x / 2) $ is expanded into a Laurent series of $ 1 - x^2 $, where the coefficients are given explicitly as combinations of zeta function of even integers. This is used to achieve a sequence of upper and lower bounds which are very precise even at the poles $ x = 1, -1 $.
Similar results are obtained for other trigonometric functions with poles.
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