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DLMF:18.12.E11 - MaRDI portal

DLMF:18.12.E11 (Q6350)

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DLMF:18.12.E11
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    Statements

    DLMF defining formula
    1 1 - 2 ⁢ x ⁢ z + z 2 = ∑ n = 0 ∞ P n ⁡ ( x ) ⁢ z n , 1 1 2 𝑥 𝑧 superscript 𝑧 2 superscript subscript 𝑛 0 Legendre-spherical-polynomial 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\frac{1}{\sqrt{1-2xz+z^{2}}}=\sum_{n=0}^{\infty}P_% {n}\left(x\right)z^{n},}}
    0 references
    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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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1jdec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1jdec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1idec
    0 references

    Identifiers

     
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