DLMF:14.5.E13 (Q4725): 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.m2acdec

Revision as of 01:22, 2 January 2020

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DLMF:14.5.E13
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    Statements

    Defining formula
    𝖰 ν 1 / 2 ⁡ ( cos ⁡ θ ) = - ( π 2 ⁢ sin ⁡ θ ) 1 / 2 ⁢ sin ⁡ ( ( ν + 1 2 ) ⁢ θ ) , Ferrers-Legendre-Q-first-kind 1 2 𝜈 𝜃 superscript 𝜋 2 𝜃 1 2 𝜈 1 2 𝜃 {\displaystyle{\displaystyle\mathsf{Q}^{1/2}_{\nu}\left(\cos\theta\right)=-% \left(\frac{\pi}{2\sin\theta}\right)^{1/2}\sin\left(\left(\nu+\tfrac{1}{2}% \right)\theta\right),}}
    0 references
    DLMF id
    DLMF:14.5.E13
    0 references
    Symbols used
    Ferrers function of the second kind
    Defining formula
    𝖰 ν μ ⁡ ( x ) Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E2.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
    0 references
     
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