# Tagged Questions

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### Definite Integral Arising from a Double Integral

I gave an integral to a student. She reported back to me that she could not do it. I've tried a couple of approaches and have failed. I imagine it is fairly easy. It's a double integral. And, no ...
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### Integral of Hermite polynomial multiplied by $\exp(-x^2/2)$

What is the value of $\int_{-\infty}^{\infty}e^{-\frac{x^2}{2}}H_n(x)dx$ where $H_n(x)$ is the $n^{\small\mbox{th}}$ Hermite Polynomial (physicist's convention)?
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### How to evaluate the following integral using hypergeometric function?

May I know how this integral was evaluated using hypergeometric function? $$\int \sin^n x\ dx$$ Wolframalpha showed this result but with no steps Thanks in advance.
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### Definite integral with $\mathrm{Si}$ in integrand

Does the function $$f(t) = \int_0^{\sqrt{3}} (x^2-1) \;\mathrm{Si}((x^2-1)\,t)\; \mathrm{d}x$$ have a representation in terms of elementary functions of $t$ for real, positive $t$? Here, ...
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### Can this function be expressed in terms of other well-known functions?

Consider the function $$f(a) = \int^1_0 \frac {t-1}{t^a-1}dt$$ Can this function be expressed in terms of 'well-known' functions for integer values of $a$? I know that it can be relatively simply ...
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### Evaluation of an integral involving the Lambert W function

Wikipedia claims that $$\int_0^\infty W\left(\frac{1}{x^2}\right) \,\text dx=\sqrt{2\pi}$$ and a numerical computation seems to confirm this. How can this result be proven?
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### Integral of the square of the Bessel Function

Has anyone ever solved the integral of square of Bessel and Neumann functions? This is for standing wave analysis on a cylindrical object. I need to integrate $(AJ(kr) + BY(kr))^2$ from $r=a$ to ...
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### Advice on an integral involving the error function

I'd like to calculate the following integral: $$\int^{\infty}_{0} \mathrm{erf}\left(\frac{\alpha}{\sqrt{1+x}} - \frac{\sqrt{1+x}}{\beta}\right) \exp\left(-\frac{x}{\gamma}\right)\, dx,$$ where ...
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### Error Function limit

$$\prod_{n=1}^{\infty}{\frac{2}{\sqrt{\pi}}\int_0^n e^{-x^{2}} \mathrm{d}x} \approx 0.83874$$ Is it a known constant? I couldn't find anything about it. Do you know ways to calculate the value ...