DLMF:30.6.E5 (Q8864)

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DLMF:30.6.E5
No description defined

    Statements

    Defining formula
    𝑄𝑠 n m ⁡ ( x ± i ⁢ 0 , γ 2 ) = ( ∓ i ) m ⁢ ( 𝖰𝗌 n m ⁡ ( x , γ 2 ) ∓ 1 2 ⁢ i ⁢ π ⁢ 𝖯𝗌 n m ⁡ ( x , γ 2 ) ) . spheroidal-wave-Qs 𝑚 𝑛 plus-or-minus 𝑥 imaginary-unit 0 superscript 𝛾 2 superscript minus-or-plus imaginary-unit 𝑚 minus-or-plus spheroidal-wave-on-cut-Qs 𝑚 𝑛 𝑥 superscript 𝛾 2 1 2 imaginary-unit 𝜋 spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 {\displaystyle{\displaystyle\mathit{Qs}^{m}_{n}\left(x\pm\mathrm{i}0,\gamma^{2% }\right)={(\mp\mathrm{i})^{m}\left(\mathsf{Qs}^{m}_{n}\left(x,\gamma^{2}\right% )\mp\tfrac{1}{2}\mathrm{i}\pi\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)% \right)}.}}
    0 references
    DLMF id
    DLMF:30.6.E5
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    Q12423
    Defining formula
    𝑄𝑠 n m ⁡ ( z , γ 2 ) spheroidal-wave-Qs 𝑚 𝑛 𝑧 superscript 𝛾 2 {\displaystyle{\displaystyle\mathit{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{z},% \NVar{\gamma^{2}}\right)}}
    xml-id
    C30.S6.p1.m2acdec
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    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
    Q12421
    Defining formula
    𝖰𝗌 n m ⁡ ( x , γ 2 ) spheroidal-wave-on-cut-Qs 𝑚 𝑛 𝑥 superscript 𝛾 2 {\displaystyle{\displaystyle\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},% \NVar{\gamma^{2}}\right)}}
    xml-id
    C30.S5.m1adec
    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.m1ddec
    0 references
     
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