DLMF:14.6.E6 (Q4748): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11447 / rank
 
Normal rank
Property / Symbols used: Q11447 / qualifier
 
Defining formula:

P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}

\assLegendreP[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreP[0]{\nu}@{z}
Property / Symbols used: Q11447 / qualifier
 
xml-id: C14.S2.SS2.p2.m3aadec

Revision as of 01:27, 2 January 2020

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DLMF:14.6.E6
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    Statements

    Defining formula
    𝖯 ν - m ⁡ ( x ) = ( 1 - x 2 ) - m / 2 ⁢ ∫ x 1 … ⁢ ∫ x 1 P ν ⁡ ( x ) ⁢ ( d x ) m . Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript 1 superscript 𝑥 2 𝑚 2 superscript subscript 𝑥 1 … superscript subscript 𝑥 1 shorthand-Legendre-P-first-kind 𝜈 𝑥 superscript 𝑥 𝑚 {\displaystyle{\displaystyle\mathsf{P}^{-m}_{\nu}\left(x\right)=\left(1-x^{2}% \right)^{-m/2}\int_{x}^{1}\!\dots\!\int_{x}^{1}P_{\nu}\left(x\right)\left(\!% \mathrm{d}x\right)^{m}.}}
    0 references
    DLMF id
    DLMF:14.6.E6
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11447
    Defining formula
    P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m3aadec
    0 references
     
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