DLMF:14.7.E21 (Q4773): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11595 / rank
 
Normal rank
Property / Symbols used: Q11595 / qualifier
 
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)}}

\FerrersP[]{\NVar{\nu}}@{\NVar{x}}=\FerrersP[0]{\nu}@{x}
Property / Symbols used: Q11595 / qualifier
 
xml-id: C14.S2.SS2.p2.m2acdec

Revision as of 01:31, 2 January 2020

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DLMF:14.7.E21
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    Statements

    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
    DLMF id
    DLMF:14.7.E21
    0 references
    Symbols used
    Q11595
    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
     
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