DLMF:14.18.E5 (Q4906): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11481 / rank
 
Normal rank
Property / Symbols used: Q11481 / qualifier
 
test:

P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11481 / qualifier
 
xml-id: C14.S21.SS1.p1.m1aadec

Revision as of 12:28, 2 January 2020

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DLMF:14.18.E5
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    Statements

    test
    Q ν ⁡ ( cosh ⁡ ξ 1 ⁢ cosh ⁡ ξ 2 - sinh ⁡ ξ 1 ⁢ sinh ⁡ ξ 2 ⁢ cos ⁡ ϕ ) = P ν ⁡ ( cosh ⁡ ξ 1 ) ⁢ Q ν ⁡ ( cosh ⁡ ξ 2 ) + 2 ⁢ ∑ m = 1 ∞ ( - 1 ) m ⁢ P ν - m ⁡ ( cosh ⁡ ξ 1 ) ⁢ Q ν m ⁡ ( cosh ⁡ ξ 2 ) ⁢ cos ⁡ ( m ⁢ ϕ ) . shorthand-Legendre-Q-second-kind 𝜈 subscript 𝜉 1 subscript 𝜉 2 subscript 𝜉 1 subscript 𝜉 2 italic-ϕ shorthand-Legendre-P-first-kind 𝜈 subscript 𝜉 1 shorthand-Legendre-Q-second-kind 𝜈 subscript 𝜉 2 2 superscript subscript 𝑚 1 superscript 1 𝑚 Legendre-P-first-kind 𝑚 𝜈 subscript 𝜉 1 Legendre-Q-second-kind 𝑚 𝜈 subscript 𝜉 2 𝑚 italic-ϕ {\displaystyle{\displaystyle Q_{\nu}\left(\cosh\xi_{1}\cosh\xi_{2}-\sinh\xi_{1% }\sinh\xi_{2}\cos\phi\right)=P_{\nu}\left(\cosh\xi_{1}\right)Q_{\nu}\left(% \cosh\xi_{2}\right)+2\sum_{m=1}^{\infty}(-1)^{m}P^{-m}_{\nu}\left(\cosh\xi_{1}% \right)Q^{m}_{\nu}\left(\cosh\xi_{2}\right)\cos\left(m\phi\right).}}
    0 references
    DLMF id
    DLMF:14.18.E5
    0 references
    Symbols used
    Q11481
    test
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1aadec
    0 references
     
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