DLMF:14.30.E1 (Q4963)

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DLMF:14.30.E1
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    Defining formula
    Y l , m ⁡ ( θ , ϕ ) = ( ( l - m ) ! ⁢ ( 2 ⁢ l + 1 ) 4 ⁢ π ⁢ ( l + m ) ! ) 1 / 2 ⁢ e i ⁢ m ⁢ ϕ ⁢ 𝖯 l m ⁡ ( cos ⁡ θ ) , spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ superscript 𝑙 𝑚 2 𝑙 1 4 𝜋 𝑙 𝑚 1 2 superscript 𝑒 𝑖 𝑚 italic-ϕ Ferrers-Legendre-P-first-kind 𝑚 𝑙 𝜃 {\displaystyle{\displaystyle Y_{{l},{m}}\left(\theta,\phi\right)=\left(\frac{(% l-m)!(2l+1)}{4\pi(l+m)!}\right)^{1/2}e^{im\phi}\mathsf{P}^{m}_{l}\left(\cos% \theta\right),}}
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    DLMF id
    DLMF:14.30.E1
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