2.10.E33 (Q991): Difference between revisions

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Revision as of 18:00, 11 July 2023

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2.10.E33
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    Statements

    DLMF defining formula
    f ⁢ ( z ) ≡ 1 ( 1 - 2 ⁢ z ⁢ cos ⁡ α + z 2 ) 1 / 2 = ∑ n = 0 ∞ P n ⁡ ( cos ⁡ α ) ⁢ z n , equal-by definition 𝑓 𝑧 1 superscript 1 2 𝑧 𝛼 superscript 𝑧 2 1 2 superscript subscript 𝑛 0 Legendre-spherical-polynomial 𝑛 𝛼 superscript 𝑧 𝑛 {\displaystyle{\displaystyle f(z)\equiv\frac{1}{(1-2z\cos\alpha+z^{2})^{1/2}}=% \sum_{n=0}^{\infty}P_{n}\left(\cos\alpha\right)z^{n},}}
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    Symbols used
    Legendre polynomial
    DLMF defining formula
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2adec
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    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    Q10743
    DLMF defining formula
    ≡ equal-by definition {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p1.t1.r9.m2adec
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    analytic function
    DLMF defining formula
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S10.XMD13.m1edec
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    Identifiers

     
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