DLMF:28.6.E26 (Q8260)

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DLMF:28.6.E26
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    Statements

    Defining formula
    ce m ⁡ ( z , q ) = cos ⁡ m ⁢ z - q 4 ⁢ ( 1 m + 1 ⁢ cos ⁡ ( m + 2 ) ⁢ z - 1 m - 1 ⁢ cos ⁡ ( m - 2 ) ⁢ z ) + q 2 32 ⁢ ( 1 ( m + 1 ) ⁢ ( m + 2 ) ⁢ cos ⁡ ( m + 4 ) ⁢ z + 1 ( m - 1 ) ⁢ ( m - 2 ) ⁢ cos ⁡ ( m - 4 ) ⁢ z - 2 ⁢ ( m 2 + 1 ) ( m 2 - 1 ) 2 ⁢ cos ⁡ m ⁢ z ) + ⋯ . Mathieu-ce 𝑚 𝑧 𝑞 𝑚 𝑧 𝑞 4 1 𝑚 1 𝑚 2 𝑧 1 𝑚 1 𝑚 2 𝑧 superscript 𝑞 2 32 1 𝑚 1 𝑚 2 𝑚 4 𝑧 1 𝑚 1 𝑚 2 𝑚 4 𝑧 2 superscript 𝑚 2 1 superscript superscript 𝑚 2 1 2 𝑚 𝑧 ⋯ {\displaystyle{\displaystyle\mathrm{ce}_{m}\left(z,q\right)=\cos mz-\frac{q}{4% }\left(\frac{1}{m+1}\cos(m+2)z-\frac{1}{m-1}\cos(m-2)z\right)+\frac{q^{2}}{32}% \left(\frac{1}{(m+1)(m+2)}\cos(m+4)z+\frac{1}{(m-1)(m-2)}\cos(m-4)z-\frac{2(m^% {2}+1)}{(m^{2}-1)^{2}}\cos mz\right)+\cdots.}}
    0 references
    DLMF id
    DLMF:28.6.E26
    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.m7acdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1bdec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1xdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1edec
    0 references
     
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