DLMF:28.12.E6 (Q8303)

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DLMF:28.12.E6
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    Statements

    Defining formula
    me ν ⁡ ( z + π , q ) = e π ⁢ i ⁢ ν ⁢ me ν ⁡ ( z , q ) , Mathieu-me 𝜈 𝑧 𝜋 𝑞 superscript 𝑒 𝜋 imaginary-unit 𝜈 Mathieu-me 𝜈 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{me}_{\nu}\left(z+\pi,q\right)=e^{\pi% \mathrm{i}\nu}\mathrm{me}_{\nu}\left(z,q\right),}}
    0 references
    DLMF id
    DLMF:28.12.E6
    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.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1cdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1adec
    0 references
    Q12278
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C28.S1.XMD7.m1ddec
    0 references
     
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