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DLMF:14.7.E21 - MaRDI portal

DLMF:14.7.E21 (Q5470)

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DLMF:14.7.E21
No description defined

    Statements

    DLMF defining formula
    ∑ n = 0 ∞ 𝖯 n ⁡ ( x ) ⁢ h - n - 1 = ( 1 - 2 ⁢ x ⁢ h + h 2 ) - 1 / 2 . superscript subscript 𝑛 0 shorthand-Ferrers-Legendre-P-first-kind 𝑛 𝑥 superscript ℎ 𝑛 1 superscript 1 2 𝑥 ℎ superscript ℎ 2 1 2 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\mathsf{P}_{n}\left(x\right)h^{% -n-1}=\left(1-2xh+h^{2}\right)^{-1/2}.}}
    0 references
    Symbols used
    Q11566
    DLMF defining formula
    𝖯 ν ⁡ ( x ) = 𝖯 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 Ferrers-Legendre-P-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{P}^{0}_{\nu}\left(x\right)}}
    xml-id
    C14.S2.SS2.p2.m2acdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1tdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1rdec
    0 references
    variable
    DLMF defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C14.S7.XMD2.m1bdec
    0 references

    Identifiers

     
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