DLMF:28.2.E32 (Q8178)

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DLMF:28.2.E32
No description defined

    Statements

    Defining formula
    ∫ 0 2 ⁢ π se m ⁡ ( x , q ) ⁢ se n ⁡ ( x , q ) ⁢ d x = 0 , superscript subscript 0 2 𝜋 Mathieu-se 𝑚 𝑥 𝑞 Mathieu-se 𝑛 𝑥 𝑞 𝑥 0 {\displaystyle{\displaystyle\int_{0}^{2\pi}\mathrm{se}_{m}\left(x,q\right)% \mathrm{se}_{n}\left(x,q\right)\mathrm{d}x=0,}}
    0 references
    DLMF id
    DLMF:28.2.E32
    0 references
    constraint
    n ≠ m 𝑛 𝑚 {\displaystyle{\displaystyle n\neq m}}
    0 references
    Symbols used
    Q12286
    Defining formula
    se n ⁡ ( z , q ) Mathieu-se 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m8acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ardec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1adec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1zdec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1pdec
    0 references
    Q12285
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C28.S1.XMD4.m1bdec
    0 references
     
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