How does one arrive at the equation(adsbygoogle = window.adsbygoogle || []).push({});

$$\bigg( (1-z^2) \frac{d^2}{dz^2} - 2z \frac{d}{dz} + l(l+1) - \frac{m^2}{1-z^2} \bigg) P(z) = 0$$

Solving this equation for ##P(z)## is one step in deriving the spherical harmonics "##Y^{m}{}_{l}(\theta, \phi)##".

The problem is that the book I'm following doesn't show how to arrive at the above equation. It shows how to arrive at it only for the special case ##m=0##.

I've tried googling "Associate Legendre's equation" and "Legendre's general equationderivation" but it seems there's no such derivation on web.

**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!

# I Spherical harmonics

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Spherical harmonics | Date |
---|---|

I Can the Schrodinger equation satisfy Laplace's equation? | Feb 22, 2018 |

I Spherical Harmonics from operator analysis | Jul 31, 2017 |

I Understanding the Form of the Y(2,0) Spherical Harmonic | Apr 7, 2017 |

I Spherical Harmonics | Mar 3, 2017 |

I Spherical Harmonics | Nov 1, 2016 |

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