DLMF:29.8.E2 (Q8705): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11595 / rank
 
Normal rank
Property / Symbols used: Q11595 / qualifier
 
Defining formula:

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)}}

\FerrersP[]{\NVar{\nu}}@{\NVar{x}}=\FerrersP[0]{\nu}@{x}
Property / Symbols used: Q11595 / qualifier
 
xml-id: C14.S2.SS2.p2.m2adec

Revision as of 01:22, 2 January 2020

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DLMF:29.8.E2
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    Statements

    Defining formula
    μ ⁢ w ⁢ ( z 1 ) ⁢ w ⁢ ( z 2 ) ⁢ w ⁢ ( z 3 ) = ∫ - 2 ⁢ K ⁡ 2 ⁢ K ⁡ 𝖯 ν ⁡ ( x ) ⁢ w ⁢ ( z ) ⁢ d z , 𝜇 𝑤 subscript 𝑧 1 𝑤 subscript 𝑧 2 𝑤 subscript 𝑧 3 superscript subscript 2 complete-elliptic-integral-first-kind-K 𝑘 2 complete-elliptic-integral-first-kind-K 𝑘 shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 𝑤 𝑧 𝑧 {\displaystyle{\displaystyle\mu w(z_{1})w(z_{2})w(z_{3})=\int_{-2K}^{2K}% \mathsf{P}_{\nu}\left(x\right)w(z)\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:29.8.E2
    0 references
    Symbols used
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11595
    Defining formula
    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
     
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