DLMF:14.15.E9 (Q4855): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2aedec

Revision as of 01:48, 2 January 2020

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DLMF:14.15.E9
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    Statements

    𝑸 ν μ ( x ) = ( π 2 ) 1 / 2 ( e μ ) ν + ( 1 / 2 ) ( 1 - α 1 + α ) μ / 2 ( 1 - α 2 ) - ( ν / 2 ) - ( 1 / 4 ) ( α 2 + η 2 α 2 ( x 2 - 1 ) + 1 ) 1 / 4 I ν + 1 2 ( μ η ) ( 1 + O ( 1 μ ) ) , associated-Legendre-black-Q 𝜇 𝜈 𝑥 superscript 𝜋 2 1 2 superscript 𝑒 𝜇 𝜈 1 2 superscript 1 𝛼 1 𝛼 𝜇 2 superscript 1 superscript 𝛼 2 𝜈 2 1 4 superscript superscript 𝛼 2 superscript 𝜂 2 superscript 𝛼 2 superscript 𝑥 2 1 1 1 4 modified-Bessel-first-kind 𝜈 1 2 𝜇 𝜂 1 Big-O 1 𝜇 {\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)=\left(% \frac{\pi}{2}\right)^{1/2}\left(\frac{e}{\mu}\right)^{\nu+(1/2)}\left(\frac{1-% \alpha}{1+\alpha}\right)^{\mu/2}\*\left(1-\alpha^{2}\right)^{-(\nu/2)-(1/4)}% \left(\frac{\alpha^{2}+\eta^{2}}{\alpha^{2}\left(x^{2}-1\right)+1}\right)^{1/4% }\*I_{\nu+\frac{1}{2}}\left(\mu\eta\right)\left(1+O\left(\frac{1}{\mu}\right)% \right),}}
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    DLMF:14.15.E9
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    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2aedec
    0 references