DLMF:30.4.E2 (Q8846)

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DLMF:30.4.E2
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    Statements

    Defining formula
    𝖯𝗌 n m ⁡ ( x , 0 ) = 𝖯 n m ⁡ ( x ) ; spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 0 Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 {\displaystyle{\displaystyle\mathsf{Ps}^{m}_{n}\left(x,0\right)=\mathsf{P}^{m}% _{n}\left(x\right);}}
    0 references
    DLMF id
    DLMF:30.4.E2
    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.m2adec
    0 references
    Q12418
    Defining formula
    𝖯𝗌 n m ⁡ ( x , γ 2 ) spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 {\displaystyle{\displaystyle\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},% \NVar{\gamma^{2}}\right)}}
    xml-id
    C30.S4.SS1.m1aadec
    0 references
    Q12419
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C30.S1.XMD2.m1adec
    0 references
    Q12408
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C30.S1.XMD4.m1adec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1adec
    0 references
     
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