DLMF:28.2.E31 (Q8177)

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DLMF:28.2.E31
No description defined

    Statements

    Defining formula
    ∫ 0 2 ⁢ π ce m ⁡ ( x , q ) ⁢ ce n ⁡ ( x , q ) ⁢ d x = 0 , superscript subscript 0 2 𝜋 Mathieu-ce 𝑚 𝑥 𝑞 Mathieu-ce 𝑛 𝑥 𝑞 𝑥 0 {\displaystyle{\displaystyle\int_{0}^{2\pi}\mathrm{ce}_{m}\left(x,q\right)% \mathrm{ce}_{n}\left(x,q\right)\mathrm{d}x=0,}}
    0 references
    DLMF id
    DLMF:28.2.E31
    0 references
    constraint
    n ≠ m 𝑛 𝑚 {\displaystyle{\displaystyle n\neq m}}
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    Symbols used
    Q12283
    Defining formula
    ce n ⁡ ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m7acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aqdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    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.m1ydec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1odec
    0 references
    Q12285
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C28.S1.XMD4.m1adec
    0 references
     
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