# Tagged Questions

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### How to get an expression for this integral(Numerically/Analytically)

I have the following problem: I need to evaluate the integral $$\int_{\cos(\alpha)}^{1} P_l(t)P_{l'}(t) dt$$ for $\alpha \in [0,\pi]$ and each combination of $l$ and $l'$, where $P_l$ is the l-th ...
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### Identity involving Fresnel integrals

In the paper E. Mehlum, Appell and the apple (nonlinear splines in space), Technical Report No. 1676 (1981), Central institute for industrial research, Oslo (reproduced in the book Mathematical ...
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### On a hypergeometric-type integral

I'm having a bit of trouble with the integral $$\int_0^1 e^{-\frac{z^2}{2}u}\frac{u^{m-\frac{1}{2}} (1-u)^{n/2} }{ \left(1+ \left(s^2-1\right)u\right)^{m+\frac{n}{2}+1}} du.$$ (Here $m$ and $n$ are ...
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Given the following contour integral $$\frac{1}{2\pi j}\int^{c+j\infty}_{c-j\infty} \frac{\Gamma(-1+a+s)\Gamma(b+s)}{\Gamma(3+a-s)}\cos(-1+a+s)\, {}_2F_1\Big(-1-a+s,-1+a+s;\frac{1}{2};z\Big) y^s\: ... 2answers 1k views ### How to do integrals involving two Bessel functions and another function? I often encounter the integrals in the following form: \int_0^\infty{\rm Bessel}(ax)\cdot{\rm Bessel}(bx)\cdot f(cx)dx, where Bessel can be J, N, H^{(1)}, H^{(2)}, I, or K; and f(x) ... 2answers 414 views ### High dimensional beta integral (a typo in Stein's book “singular integrals”) Hello, When I read Stein's book of Singular Integrals, at p. 118, there is an obvious mistake:$$ \int_{R^n} |x-y|^{-n+\alpha} ...
Consider the following integral,  {1 \over 4\pi^{2}}\int_{0}^{2\pi}\int_{0}^{2\pi} \sqrt{\, 9 -\sin^{2}\left(\theta_{1} \over 2\right) \sin^{2}\left(\theta_{2} \over 2\right)\,} \,{\rm ...