DLMF:28.12.E7 (Q8304)

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DLMF:28.12.E7
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    Statements

    Defining formula
    ∫ 0 π me ν + 2 ⁢ m ⁡ ( x , q ) ⁢ me ν + 2 ⁢ n ⁡ ( - x , q ) ⁢ d x = 0 , superscript subscript 0 𝜋 Mathieu-me 𝜈 2 𝑚 𝑥 𝑞 Mathieu-me 𝜈 2 𝑛 𝑥 𝑞 𝑥 0 {\displaystyle{\displaystyle{\int_{0}^{\pi}\mathrm{me}_{\nu+2m}\left(x,q\right% )\mathrm{me}_{\nu+2n}\left(-x,q\right)\mathrm{d}x=0,}}}
    0 references
    DLMF id
    DLMF:28.12.E7
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    constraint
    m ≠ n 𝑚 𝑛 {\displaystyle{\displaystyle m\neq n}}
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    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.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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