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DLMF:14.30.E4 - MaRDI portal

DLMF:14.30.E4 (Q5663)

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DLMF:14.30.E4
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    Statements

    DLMF defining formula
    Y l , m ⁡ ( 0 , ϕ ) = { ( 2 ⁢ l + 1 4 ⁢ π ) 1 / 2 , m = 0 , 0 , | m | = 1 , 2 , 3 , … , spherical-harmonic-Y 𝑙 𝑚 0 italic-ϕ cases superscript 2 𝑙 1 4 𝜋 1 2 𝑚 0 0 𝑚 1 2 3 … {\displaystyle{\displaystyle Y_{{l},{m}}\left(0,\phi\right)=\begin{cases}\left% (\dfrac{2l+1}{4\pi}\right)^{1/2},&m=0,\\ 0,&|m|=1,2,3,\dots,\end{cases}}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    spherical harmonic
    DLMF defining formula
    Y l , m ⁡ ( θ , ϕ ) spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ {\displaystyle{\displaystyle Y_{{\NVar{l}},{\NVar{m}}}\left(\NVar{\theta},% \NVar{\phi}\right)}}
    xml-id
    C14.S30.E1.m2abdec
    0 references
    integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S30.XMD1.m1cdec
    0 references
    nonnegative integer
    DLMF defining formula
    l 𝑙 {\displaystyle{\displaystyle l}}
    xml-id
    C14.S30.XMD2.m1cdec
    0 references

    Identifiers

     
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