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DLMF:28.4.E22 - MaRDI portal

DLMF:28.4.E22 (Q8909)

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DLMF:28.4.E22
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    Statements

    DLMF defining formula
    A m + 2 ⁢ s m ⁢ ( q ) B m + 2 ⁢ s m ⁢ ( q ) } = ( ( - 1 ) s ⁢ m ! s ! ⁢ ( m + s ) ! ⁢ ( q 4 ) s + O ⁡ ( q s + 1 ) ) ⁢ { A m m ⁢ ( q ) , B m m ⁢ ( q ) , selection subscript superscript 𝐴 𝑚 𝑚 2 𝑠 𝑞 subscript superscript 𝐵 𝑚 𝑚 2 𝑠 𝑞 superscript 1 𝑠 𝑚 𝑠 𝑚 𝑠 superscript 𝑞 4 𝑠 Big-O superscript 𝑞 𝑠 1 selection subscript superscript 𝐴 𝑚 𝑚 𝑞 subscript superscript 𝐵 𝑚 𝑚 𝑞 {\displaystyle{\displaystyle\rselection{A^{m}_{m+2s}(q)\\ B^{m}_{m+2s}(q)}=\left(\dfrac{(-1)^{s}m!}{s!(m+s)!}\left(\frac{q}{4}\right)^{s% }+O\left(q^{s+1}\right)\right)\lselection{A^{m}_{m}(q),\\ B^{m}_{m}(q),}}}
    0 references
    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1tdec
    0 references
    parameter
    DLMF defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1qdec
    0 references
    Fourier coefficient
    DLMF defining formula
    A m ⁢ ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}}
    xml-id
    C28.S4.XMD1.m1ldec
    0 references
    Fourier coefficient
    DLMF defining formula
    B m ⁢ ( q ) subscript 𝐵 𝑚 𝑞 {\displaystyle{\displaystyle B_{m}(q)}}
    xml-id
    C28.S4.XMD2.m1kdec
    0 references

    Identifiers

     
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