Consider an integral of the type ## \int_0^{a} \int_0^{\pi} g(\rho,\varphi,\theta) \rho d\varphi d\rho ##. As you can see, the integral is w.r.t. cylindrical coordinates on a plane but the integrand is also a function of ##\theta## which is a spherical coordinate. So for evaluating it, there are two options: 1) Write ## \theta ## in terms of cylindrical coordinates. 2) Transform the integral to spherical coordinates. The first option makes the integral an intractable mess. But the second option seems nice because the integrand(in spherical coordinates) contains a factor of the form ## (1-2xt+t^2)^{-\frac 1 2} ## and so the integral can be done using Legendre polynomials and spherical harmonics. But I don't know how I should transform the integral from cylindrical to spherical coordinates. Can anyone help?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks

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# Transformation of integrals

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