DLMF:28.14.E10 (Q8324)

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DLMF:28.14.E10
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    Statements

    Defining formula
    c 2 ⁢ m ν ⁢ ( q ) = ( ( - 1 ) m ⁢ q m ⁢ Γ ⁡ ( ν + 1 ) m ! ⁢  2 2 ⁢ m ⁢ Γ ⁡ ( ν + m + 1 ) + O ⁡ ( q m + 2 ) ) ⁢ c 0 ν ⁢ ( q ) . superscript subscript 𝑐 2 𝑚 𝜈 𝑞 superscript 1 𝑚 superscript 𝑞 𝑚 Euler-Gamma 𝜈 1 𝑚 superscript  2 2 𝑚 Euler-Gamma 𝜈 𝑚 1 Big-O superscript 𝑞 𝑚 2 superscript subscript 𝑐 0 𝜈 𝑞 {\displaystyle{\displaystyle c_{2m}^{\nu}(q)=\left(\frac{(-1)^{m}q^{m}\Gamma% \left(\nu+1\right)}{m!\,2^{2m}\Gamma\left(\nu+m+1\right)}+O\left(q^{m+2}\right% )\right)c_{0}^{\nu}(q).}}
    0 references
    DLMF id
    DLMF:28.14.E10
    0 references
    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
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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