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DLMF:28.2.E35 - MaRDI portal

DLMF:28.2.E35 (Q8874)

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DLMF:28.2.E35
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    Statements

    DLMF defining formula
    ce 2 ⁢ n + 1 ⁡ ( z , - q ) = ( - 1 ) n ⁢ se 2 ⁢ n + 1 ⁡ ( 1 2 ⁢ π - z , q ) , Mathieu-ce 2 𝑛 1 𝑧 𝑞 superscript 1 𝑛 Mathieu-se 2 𝑛 1 1 2 𝜋 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{2n+1}\left(z,-q\right)=(-1)^{n}% \mathrm{se}_{2n+1}\left(\tfrac{1}{2}\pi-z,q\right),}}
    0 references
    Symbols used
    Q12286
    DLMF 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.m7afdec
    0 references
    Q12289
    DLMF 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.m8aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2audec
    0 references
    parameter
    DLMF defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1acdec
    0 references
    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1sdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1jdec
    0 references

    Identifiers

     
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