DLMF:28.14.E1 (Q8314)

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DLMF:28.14.E1
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    Statements

    Defining formula
    me ν ⁡ ( z , q ) = ∑ m = - ∞ ∞ c 2 ⁢ m ν ⁢ ( q ) ⁢ e i ⁢ ( ν + 2 ⁢ m ) ⁢ z , Mathieu-me 𝜈 𝑧 𝑞 superscript subscript 𝑚 subscript superscript 𝑐 𝜈 2 𝑚 𝑞 superscript 𝑒 imaginary-unit 𝜈 2 𝑚 𝑧 {\displaystyle{\displaystyle\mathrm{me}_{\nu}\left(z,q\right)=\sum_{m=-\infty}% ^{\infty}c^{\nu}_{2m}(q)e^{\mathrm{i}(\nu+2m)z},}}
    0 references
    DLMF id
    DLMF:28.14.E1
    0 references
    Symbols used
    Q12299
    Defining formula
    me n ⁡ ( z , q ) Mathieu-me 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S12.SS2.p2.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1dec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1dec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1dec
    0 references
    Q12278
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C28.S1.XMD7.m1dec
    0 references
    Q12300
    Defining formula
    c 2 ⁢ m ⁢ ( q ) subscript 𝑐 2 𝑚 𝑞 {\displaystyle{\displaystyle c_{2m}(q)}}
    xml-id
    C28.S14.XMD1.m1dec
    0 references
     
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