DLMF:14.23.E4 (Q4950)

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DLMF:14.23.E4
No description defined

    Statements

    Defining formula
    𝖯 ν μ ⁡ ( x ) = e ± μ ⁢ π ⁢ i / 2 ⁢ P ν μ ⁡ ( x ± i ⁢ 0 ) , Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 superscript 𝑒 plus-or-minus 𝜇 𝜋 𝑖 2 Legendre-P-first-kind 𝜇 𝜈 plus-or-minus 𝑥 𝑖 0 {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(x\right)=e^{\pm\mu\pi i% /2}P^{\mu}_{\nu}\left(x\pm i0\right),}}
    0 references
    DLMF id
    DLMF:14.23.E4
    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.m2abdec
    0 references
    Q11481
    Defining formula
    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
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1cdec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1cdec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1cdec
    0 references
     
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