Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The completeness relation for the spherical harmonics is:

$$\sum_{l=0}^{\infty} \sum_{m=-l}^{l} Y_{lm}^*\left(\theta_1,\phi_1\right)Y_{lm}\left(\theta_2,\phi_2\right) = \delta\left(\phi_1-\phi_2\right)\delta\left(\theta_1-\theta_2\right)$$

Any ideas what the same sum without the conjugation would evaluate to? I.e. what is:

$$\sum_{l=0}^{\infty} \sum_{m=-l}^{l} Y_{lm}\left(\theta_1,\phi_1\right)Y_{lm}\left(\theta_2,\phi_2\right) =\ ?$$

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.