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i have a question regarding the addition theorem for spherical harmonics. In JD Jackson book pg 110 for e.g. the addition theorem is given as:

[tex]

P_{L}(cos(\gamma))=\frac{4\pi}{2L+1}\sum_{m=-L}^{L}Y^{*}_{Lm}(\theta',\phi')Y_{Lm}(\theta,\phi)

[/tex]

where [tex] cos(\gamma)=cos\theta cos\theta' + sin\theta sin\theta' cos(\phi-\phi') [/tex]. The 2 coordinate system[tex] (r,\theta,\phi) [/tex]and[tex] (r',\theta',\phi')[/tex] have an angle [tex]\gamma [/tex] between them.

My question is:

How can we express [tex]Y_{Lm}(\theta',\phi') [/tex] in terms of [tex]Y_{Lm}(\theta,\phi) [/tex] ?

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# Addition Theorem for Spherical Harmonics

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