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DLMF:28.20.E6 - MaRDI portal

DLMF:28.20.E6 (Q9031)

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DLMF:28.20.E6
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    Statements

    DLMF defining formula
    Fe n ⁡ ( z , q ) = ∓ i ⁢ fe n ⁡ ( ± i ⁢ z , q ) , modified-Mathieu-Fe 𝑛 𝑧 𝑞 minus-or-plus imaginary-unit Mathieu-fe 𝑛 plus-or-minus imaginary-unit 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Fe}_{n}\left(z,q\right)=\mp\mathrm{i}% \mathrm{fe}_{n}\left(\pm\mathrm{i}z,q\right),}}
    0 references
    constraint
    n = 0 , 1 , … 𝑛 0 1 … {\displaystyle{\displaystyle n=0,1,\dots}}
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    Symbols used
    second solution, Mathieu’s equation
    DLMF defining formula
    fe n ⁡ ( z , q ) Mathieu-fe 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S5.E1.m2adec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    parameter
    DLMF defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1edec
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    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1dec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1edec
    0 references

    Identifiers

     
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