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Sinc function

402 bytes added, 13:00, 4 September 2011
Key data
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| [[point of inflection|points of inflection]] || {{fillin}}
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| important symmetries || The function is an [[even function]], i.e., the graph has symmetry about the <math>y</math>-axis.
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| [[derivative]] || <math>\operatorname{sinc}'x = \left\lbrace \begin{array}{rl} 0, & x = 0 \\ \frac{x \cos x - \sin x}{x^2}, & x \ne 0\\\end{array}\right.</math>
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| [[antiderivative]] || the [[sine integral]] (''this is defined as the antiderivative of the sinc function that takes the value 0 at 0'')
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| [[power series]] and [[Taylor series]] || The power series about 0 (which is also the Taylor series) is<br><math>\sum_{k=0}^\infty \frac{(-1)^kx^{2k}}(2k + 1)!} = 1 - \frac{x^2}{3!} + \frac{x^4}{5!} - \dots</math><br>The power series converges globally to the function.
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