DLMF:30.6.E4 (Q8863)

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DLMF:30.6.E4
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    Statements

    Defining formula
    𝑃𝑠 n m ⁡ ( x ± i ⁢ 0 , γ 2 ) = ( ∓ i ) m ⁢ 𝖯𝗌 n m ⁡ ( x , γ 2 ) , spheroidal-wave-Ps 𝑚 𝑛 plus-or-minus 𝑥 imaginary-unit 0 superscript 𝛾 2 superscript minus-or-plus imaginary-unit 𝑚 spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 {\displaystyle{\displaystyle\mathit{Ps}^{m}_{n}\left(x\pm\mathrm{i}0,\gamma^{2% }\right)=(\mp\mathrm{i})^{m}\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right),}}
    0 references
    DLMF id
    DLMF:30.6.E4
    0 references
    Symbols used
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q12422
    Defining formula
    𝑃𝑠 n m ⁡ ( z , γ 2 ) spheroidal-wave-Ps 𝑚 𝑛 𝑧 superscript 𝛾 2 {\displaystyle{\displaystyle\mathit{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{z},% \NVar{\gamma^{2}}\right)}}
    xml-id
    C30.S6.p1.m1acdec
    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.m1adec
    0 references
    Q12419
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C30.S1.XMD2.m1dec
    0 references
     
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