DLMF:28.4.E2 (Q8187)

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DLMF:28.4.E2
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    Statements

    Defining formula
    ce 2 ⁢ n + 1 ⁡ ( z , q ) = ∑ m = 0 ∞ A 2 ⁢ m + 1 2 ⁢ n + 1 ⁢ ( q ) ⁢ cos ⁡ ( 2 ⁢ m + 1 ) ⁢ z , Mathieu-ce 2 𝑛 1 𝑧 𝑞 superscript subscript 𝑚 0 subscript superscript 𝐴 2 𝑛 1 2 𝑚 1 𝑞 2 𝑚 1 𝑧 {\displaystyle{\displaystyle\mathrm{ce}_{2n+1}\left(z,q\right)=\sum_{m=0}^{% \infty}A^{2n+1}_{2m+1}(q)\cos(2m+1)z,}}
    0 references
    DLMF id
    DLMF:28.4.E2
    0 references
    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.m7aadec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1adec
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    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1adec
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    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1adec
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    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1adec
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    Q12287
    Defining formula
    A m ⁢ ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}}
    xml-id
    C28.S4.XMD1.m1adec
    0 references
     
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