DLMF:28.11.E5 (Q8295)

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DLMF:28.11.E5
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    Statements

    Defining formula
    cos ⁡ ( 2 ⁢ m + 1 ) ⁢ z = ∑ n = 0 ∞ A 2 ⁢ m + 1 2 ⁢ n + 1 ⁢ ( q ) ⁢ ce 2 ⁢ n + 1 ⁡ ( z , q ) , 2 𝑚 1 𝑧 superscript subscript 𝑛 0 superscript subscript 𝐴 2 𝑚 1 2 𝑛 1 𝑞 Mathieu-ce 2 𝑛 1 𝑧 𝑞 {\displaystyle{\displaystyle\cos(2m+1)z=\sum_{n=0}^{\infty}A_{2m+1}^{2n+1}(q)% \mathrm{ce}_{2n+1}\left(z,q\right),}}
    0 references
    DLMF id
    DLMF:28.11.E5
    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.m7addec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    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.m1ddec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1ddec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1cdec
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    Q12287
    Defining formula
    A m ⁢ ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}}
    xml-id
    C28.S4.XMD1.m1bdec
    0 references
     
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