DLMF:28.8.E4 (Q8269)

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DLMF:28.8.E4
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    Statements

    Defining formula
    U m ⁢ ( ξ ) ∼ D m ⁡ ( ξ ) - 1 2 6 ⁢ h ⁢ ( D m + 4 ⁡ ( ξ ) - 4 ! ⁢ ( m 4 ) ⁢ D m - 4 ⁡ ( ξ ) ) + 1 2 13 ⁢ h 2 ⁢ ( D m + 8 ⁡ ( ξ ) - 2 5 ⁢ ( m + 2 ) ⁢ D m + 4 ⁡ ( ξ ) + 4 ! ⁢  2 5 ⁢ ( m - 1 ) ⁢ ( m 4 ) ⁢ D m - 4 ⁡ ( ξ ) + 8 ! ⁢ ( m 8 ) ⁢ D m - 8 ⁡ ( ξ ) ) + ⋯ , asymptotic-expansion subscript 𝑈 𝑚 𝜉 Whittaker-D 𝑚 𝜉 1 superscript 2 6 ℎ Whittaker-D 𝑚 4 𝜉 4 binomial 𝑚 4 Whittaker-D 𝑚 4 𝜉 1 superscript 2 13 superscript ℎ 2 Whittaker-D 𝑚 8 𝜉 superscript 2 5 𝑚 2 Whittaker-D 𝑚 4 𝜉 4 superscript  2 5 𝑚 1 binomial 𝑚 4 Whittaker-D 𝑚 4 𝜉 8 binomial 𝑚 8 Whittaker-D 𝑚 8 𝜉 ⋯ {\displaystyle{\displaystyle U_{m}(\xi)\sim D_{m}\left(\xi\right)-\frac{1}{2^{% 6}h}\left(D_{m+4}\left(\xi\right)-4!\dbinom{m}{4}D_{m-4}\left(\xi\right)\right% )+\frac{1}{2^{13}h^{2}}\left(D_{m+8}\left(\xi\right)-2^{5}(m+2)D_{m+4}\left(% \xi\right)+4!\,2^{5}(m-1)\dbinom{m}{4}D_{m-4}\left(\xi\right)+8!\genfrac{(}{)}% {0.0pt}{}{m}{8}D_{m-8}\left(\xi\right)\right)+\cdots,}}
    0 references
    DLMF id
    DLMF:28.8.E4
    0 references
    Symbols used
    Q11515
    Defining formula
    D ν ⁡ ( z ) Whittaker-D 𝜈 𝑧 {\displaystyle{\displaystyle D_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C12.S1.p3.m6adec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
     
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