DLMF:14.12.E12 (Q4833): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11481 / rank
 
Normal rank
Property / Symbols used: Q11481 / qualifier
 
test:

P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11481 / qualifier
 
xml-id: C14.S21.SS1.p1.m1addec

Revision as of 00:44, 2 January 2020

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DLMF:14.12.E12
No description defined

    Statements

    test
    𝑸 n m ⁡ ( x ) = 1 ( n - m ) ! ⁢ P n m ⁡ ( x ) ⁢ ∫ x ∞ d t ( t 2 - 1 ) ⁢ ( P n m ⁡ ( t ) ) 2 , associated-Legendre-black-Q 𝑚 𝑛 𝑥 1 𝑛 𝑚 Legendre-P-first-kind 𝑚 𝑛 𝑥 superscript subscript 𝑥 𝑡 superscript 𝑡 2 1 superscript Legendre-P-first-kind 𝑚 𝑛 𝑡 2 {\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n}\left(x\right)=\frac{1}{(n-m% )!}P^{m}_{n}\left(x\right)\int_{x}^{\infty}\frac{\mathrm{d}t}{\left(t^{2}-1% \right)\left(\displaystyle P^{m}_{n}\left(t\right)\right)^{2}},}}
    0 references
    DLMF id
    DLMF:14.12.E12
    0 references
    constraint
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    0 references
    Symbols used
    Q11481
    test
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1addec
    0 references
     
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