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

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Transformation of integrals

Loading...

Similar Threads - Transformation integrals | Date |
---|---|

I Fredholm integral equation with separable kernel | Jul 9, 2017 |

A Inverse Laplace transform of F(s)=exp(-as) as delta(t-a) | Feb 17, 2017 |

A Inverse Laplace transform of a piecewise defined function | Feb 17, 2017 |

Non-trivial Gaussian integral | Aug 6, 2015 |

Physical insight into integrating a product of two functions | Apr 27, 2015 |

**Physics Forums - The Fusion of Science and Community**