DLMF:14.5.E11 (Q4723): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1ddec

Revision as of 01:22, 2 January 2020

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DLMF:14.5.E11
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    Statements

    𝖯 ν 1 / 2 ( cos θ ) = ( 2 π sin θ ) 1 / 2 cos ( ( ν + 1 2 ) θ ) , Ferrers-Legendre-P-first-kind 1 2 𝜈 𝜃 superscript 2 𝜋 𝜃 1 2 𝜈 1 2 𝜃 {\displaystyle{\displaystyle\mathsf{P}^{1/2}_{\nu}\left(\cos\theta\right)=% \left(\frac{2}{\pi\sin\theta}\right)^{1/2}\cos\left(\left(\nu+\tfrac{1}{2}% \right)\theta\right),}}
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    DLMF:14.5.E11
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    𝖯 ν μ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    C14.S3.E1.m2abdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2aadec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2aadec
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    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C14.S1.XMD8.m1ddec
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