Can we calculate $\int_{0}^\infty \operatorname{sinc}^{\sqrt {13}}t \text{ d}t$

Asked Feb 20 '16 at 03:32

Active Feb 20 '16 at 06:33

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I am curious if this integral has a closed form: $$\int_0^\infty \operatorname{sinc}^{\sqrt{13}}t\,dt$$

A closed form for integer exponent is given here: Evaluating $\int_0^{\infty} \text{sinc}^m(x) dx$

But what if the exponent is not an integer?($m\in\Bbb{Z^+}$, and $\sqrt{17}\not\in \Bbb{Z}^+$)

edited Apr 13 '17 at 12:20

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asked Feb 20 '16 at 03:32

have you tried differentiating with respect to $c$? – Saikat Feb 20 '16 at 05:23
I mean I read it as $\sin{c^{m}t}$. However, if there is some other function called $\sinc$, then I do not know what it does. – Saikat Feb 20 '16 at 05:24
@user230452: It's an abbreviated form of the sinus cardinalis - see https://en.wikipedia.org/wiki/Sinc_function. – J W Feb 20 '16 at 06:40

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