DLMF:14.12.E11 (Q4832): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11592 / rank
 
Normal rank
Property / Symbols used: Q11592 / qualifier
 
test:

𝑸 ν μ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}

\assLegendreOlverQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11592 / qualifier
 
xml-id: C14.S21.SS1.p1.m3abdec

Revision as of 00:44, 2 January 2020

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DLMF:14.12.E11
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    Statements

    𝑸 n m ( x ) = ( x 2 - 1 ) m / 2 2 n + 1 n ! - 1 1 ( 1 - t 2 ) n ( x - t ) n + m + 1 d t , associated-Legendre-black-Q 𝑚 𝑛 𝑥 superscript superscript 𝑥 2 1 𝑚 2 superscript 2 𝑛 1 𝑛 superscript subscript 1 1 superscript 1 superscript 𝑡 2 𝑛 superscript 𝑥 𝑡 𝑛 𝑚 1 𝑡 {\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n}\left(x\right)=\frac{\left(x% ^{2}-1\right)^{m/2}}{2^{n+1}n!}\int_{-1}^{1}\frac{\left(1-t^{2}\right)^{n}}{(x% -t)^{n+m+1}}\mathrm{d}t,}}
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    𝑸 ν μ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    C14.S21.SS1.p1.m3abdec
    0 references