DLMF:28.4.E22 (Q8216)

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DLMF:28.4.E22
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    Statements

    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
    DLMF id
    DLMF:28.4.E22
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
     
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