DLMF:28.19.E4 (Q8332): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12300 / rank
 
Normal rank
Property / Symbols used: Q12300 / qualifier
 
test:

c 2 ⁢ m ⁢ ( q ) subscript 𝑐 2 𝑚 𝑞 {\displaystyle{\displaystyle c_{2m}(q)}}

c_{2m}(q)
Property / Symbols used: Q12300 / qualifier
 
xml-id: C28.S14.XMD1.m1dec

Latest revision as of 13:59, 2 January 2020

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DLMF:28.19.E4
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    Statements

    test
    e i ⁢ ν ⁢ z = ∑ n = - ∞ ∞ c - 2 ⁢ n ν + 2 ⁢ n ⁢ ( q ) ⁢ me ν + 2 ⁢ n ⁡ ( z , q ) , superscript 𝑒 imaginary-unit 𝜈 𝑧 superscript subscript 𝑛 subscript superscript 𝑐 𝜈 2 𝑛 2 𝑛 𝑞 Mathieu-me 𝜈 2 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle e^{\mathrm{i}\nu z}=\sum_{n=-\infty}^{\infty}c^{% \nu+2n}_{-2n}(q)\mathrm{me}_{\nu+2n}\left(z,q\right),}}
    0 references
    DLMF id
    DLMF:28.19.E4
    0 references
    Symbols used
    Q12299
    test
    me n ⁡ ( z , q ) Mathieu-me 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S12.SS2.p2.m2abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q12271
    test
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1bdec
    0 references
    Q12279
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1bdec
    0 references
    Q12272
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1cdec
    0 references
    Q12278
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C28.S1.XMD7.m1cdec
    0 references
    Q12300
    test
    c 2 ⁢ m ⁢ ( q ) subscript 𝑐 2 𝑚 𝑞 {\displaystyle{\displaystyle c_{2m}(q)}}
    xml-id
    C28.S14.XMD1.m1dec
    0 references
     
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