DLMF:14.18.E1 (Q4902): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11623 / rank
 
Normal rank
Property / Symbols used: Q11623 / qualifier
 
test:

θ 1 subscript 𝜃 1 {\displaystyle{\displaystyle\theta_{1}}}

\theta_{1}
Property / Symbols used: Q11623 / qualifier
 
xml-id: C14.S18.XMD1.m1dec

Latest revision as of 12:27, 2 January 2020

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DLMF:14.18.E1
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    Statements

    test
    𝖯 ν ⁡ ( cos ⁡ θ 1 ⁢ cos ⁡ θ 2 + sin ⁡ θ 1 ⁢ sin ⁡ θ 2 ⁢ cos ⁡ ϕ ) = 𝖯 ν ⁡ ( cos ⁡ θ 1 ) ⁢ 𝖯 ν ⁡ ( cos ⁡ θ 2 ) + 2 ⁢ ∑ m = 1 ∞ ( - 1 ) m ⁢ 𝖯 ν - m ⁡ ( cos ⁡ θ 1 ) ⁢ 𝖯 ν m ⁡ ( cos ⁡ θ 2 ) ⁢ cos ⁡ ( m ⁢ ϕ ) , shorthand-Ferrers-Legendre-P-first-kind 𝜈 subscript 𝜃 1 subscript 𝜃 2 subscript 𝜃 1 subscript 𝜃 2 italic-ϕ shorthand-Ferrers-Legendre-P-first-kind 𝜈 subscript 𝜃 1 shorthand-Ferrers-Legendre-P-first-kind 𝜈 subscript 𝜃 2 2 superscript subscript 𝑚 1 superscript 1 𝑚 Ferrers-Legendre-P-first-kind 𝑚 𝜈 subscript 𝜃 1 Ferrers-Legendre-P-first-kind 𝑚 𝜈 subscript 𝜃 2 𝑚 italic-ϕ {\displaystyle{\displaystyle\mathsf{P}_{\nu}\left(\cos\theta_{1}\cos\theta_{2}% +\sin\theta_{1}\sin\theta_{2}\cos\phi\right)=\mathsf{P}_{\nu}\left(\cos\theta_% {1}\right)\mathsf{P}_{\nu}\left(\cos\theta_{2}\right)+2\sum_{m=1}^{\infty}(-1)% ^{m}\mathsf{P}^{-m}_{\nu}\left(\cos\theta_{1}\right)\mathsf{P}^{m}_{\nu}\left(% \cos\theta_{2}\right)\cos\left(m\phi\right),}}
    0 references
    DLMF id
    DLMF:14.18.E1
    0 references
    Symbols used
    Ferrers function of the first kind
    test
    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.m2adec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q11595
    test
    𝖯 ν ⁡ ( x ) = 𝖯 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 Ferrers-Legendre-P-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{P}^{0}_{\nu}\left(x\right)}}
    xml-id
    C14.S2.SS2.p2.m2adec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q11593
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1dec
    0 references
    Q11590
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1dec
    0 references
    Q11623
    test
    θ 1 subscript 𝜃 1 {\displaystyle{\displaystyle\theta_{1}}}
    xml-id
    C14.S18.XMD1.m1dec
    0 references
     
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