DLMF:14.9.E6 (Q4797): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Ferrers function of the first kind / rank
 
Normal rank
Property / Symbols used: Ferrers function of the first kind / qualifier
 
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)}}

\FerrersP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Ferrers function of the first kind / qualifier
 
xml-id: C14.S3.E1.m2addec

Revision as of 01:36, 2 January 2020

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DLMF:14.9.E6
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    Statements

    Defining formula
    π ⁢ cos ⁡ ( ν ⁢ π ) ⁢ cos ⁡ ( μ ⁢ π ) ⁢ 𝖯 ν μ ⁡ ( x ) = sin ⁡ ( ( ν + μ ) ⁢ π ) ⁢ 𝖰 ν μ ⁡ ( x ) - sin ⁡ ( ( ν - μ ) ⁢ π ) ⁢ 𝖰 - ν - 1 μ ⁡ ( x ) . 𝜋 𝜈 𝜋 𝜇 𝜋 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝜈 𝜇 𝜋 Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 𝜈 𝜇 𝜋 Ferrers-Legendre-Q-first-kind 𝜇 𝜈 1 𝑥 {\displaystyle{\displaystyle\pi\cos\left(\nu\pi\right)\cos\left(\mu\pi\right)% \mathsf{P}^{\mu}_{\nu}\left(x\right)=\sin\left((\nu+\mu)\pi\right)\mathsf{Q}^{% \mu}_{\nu}\left(x\right)-\sin\left((\nu-\mu)\pi\right)\mathsf{Q}^{\mu}_{-\nu-1% }\left(x\right).}}
    0 references
    DLMF id
    DLMF:14.9.E6
    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.m2addec
    0 references
     
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