DLMF:14.18.E8 (Q4909): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11595 / rank
 
Normal rank
Property / Symbols used: Q11595 / qualifier
 
test:

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 12:28, 2 January 2020

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DLMF:14.18.E8
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    Statements

    test
    𝖯 ν ⁡ ( - x ) = sin ⁡ ( ν ⁢ π ) π ⁢ ∑ n = 0 ∞ 2 ⁢ n + 1 ( ν - n ) ⁢ ( ν + n + 1 ) ⁢ 𝖯 n ⁡ ( x ) , shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 𝜈 𝜋 𝜋 superscript subscript 𝑛 0 2 𝑛 1 𝜈 𝑛 𝜈 𝑛 1 shorthand-Ferrers-Legendre-P-first-kind 𝑛 𝑥 {\displaystyle{\displaystyle\mathsf{P}_{\nu}\left(-x\right)=\frac{\sin\left(% \nu\pi\right)}{\pi}\sum_{n=0}^{\infty}\frac{2n+1}{(\nu-n)(\nu+n+1)}\mathsf{P}_% {n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:14.18.E8
    0 references
    constraint
    ν ∉ ℤ 𝜈 {\displaystyle{\displaystyle\nu\notin\mathbb{Z}}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10818
    test
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2adec
    0 references
    Q11245
    test
    ∉ {\displaystyle{\displaystyle\notin}}
    xml-id
    introduction.Sx4.p1.t1.r11.m2adec
    0 references
    Q11595
    test
    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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