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DLMF:28.20.E7 - MaRDI portal

DLMF:28.20.E7 (Q9032)

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DLMF:28.20.E7
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    Statements

    DLMF defining formula
    Ge n ⁑ ( z , q ) = ge n ⁑ ( Β± i ⁒ z , q ) , modified-Mathieu-Ge 𝑛 𝑧 π‘ž Mathieu-ge 𝑛 plus-or-minus imaginary-unit 𝑧 π‘ž {\displaystyle{\displaystyle\mathrm{Ge}_{n}\left(z,q\right)=\mathrm{ge}_{n}% \left(\pm\mathrm{i}z,q\right),}}
    0 references
    constraint
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}
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    Symbols used
    second solution, Mathieu’s equation
    DLMF defining formula
    ge n ⁑ ( z , q ) Mathieu-ge 𝑛 𝑧 π‘ž {\displaystyle{\displaystyle\mathrm{ge}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S5.E2.m2adec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
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    parameter
    DLMF defining formula
    q = h 2 π‘ž superscript β„Ž 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1fdec
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    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1fdec
    0 references
     
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