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

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

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2aadec

Revision as of 01:14, 2 January 2020

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DLMF:14.3.E11
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    Statements

    Defining formula
    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),}}
    0 references
    DLMF id
    DLMF:14.3.E11
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
     
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