DLMF:14.3.E11 (Q4700): Difference between revisions

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

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
Defining formula:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1fdec
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.m1idec
Property / Symbols used
 
Property / Symbols used: Q11594 / rank
 
Normal rank
Property / Symbols used: Q11594 / qualifier
 
Defining formula:

w 2 subscript 𝑤 2 {\displaystyle{\displaystyle w_{2}}}

w_{2}
Property / Symbols used: Q11594 / qualifier
 
xml-id: C14.S3.XMD1.m1dec

Latest revision as of 01:14, 2 January 2020

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DLMF:14.3.E11
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    Statements

    𝖯 ν μ ( x ) = cos ( 1 2 ( ν + μ ) π ) w 1 ( ν , μ , x ) + sin ( 1 2 ( ν + μ ) π ) w 2 ( ν , μ , x ) , Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 1 2 𝜈 𝜇 𝜋 subscript 𝑤 1 𝜈 𝜇 𝑥 1 2 𝜈 𝜇 𝜋 subscript 𝑤 2 𝜈 𝜇 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(x\right)=\cos\left(% \tfrac{1}{2}(\nu+\mu)\pi\right)w_{1}(\nu,\mu,x)+\sin\left(\tfrac{1}{2}(\nu+\mu% )\pi\right)w_{2}(\nu,\mu,x),}}
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    DLMF:14.3.E11
    0 references
    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.m2acdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2acdec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2aadec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2aadec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C14.S1.XMD1.m1jdec
    0 references
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    C14.S1.XMD7.m1fdec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C14.S1.XMD8.m1idec
    0 references
    w 2 subscript 𝑤 2 {\displaystyle{\displaystyle w_{2}}}
    C14.S3.XMD1.m1dec
    0 references