DLMF:12.9.E1 (Q4150)

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DLMF:12.9.E1
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    Statements

    test
    U ⁡ ( a , z ) ∼ e - 1 4 ⁢ z 2 ⁢ z - a - 1 2 ⁢ ∑ s = 0 ∞ ( - 1 ) s ⁢ ( 1 2 + a ) 2 ⁢ s s ! ⁢ ( 2 ⁢ z 2 ) s , asymptotic-expansion parabolic-U 𝑎 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 superscript 𝑧 𝑎 1 2 superscript subscript 𝑠 0 superscript 1 𝑠 Pochhammer 1 2 𝑎 2 𝑠 𝑠 superscript 2 superscript 𝑧 2 𝑠 {\displaystyle{\displaystyle U\left(a,z\right)\sim e^{-\frac{1}{4}z^{2}}z^{-a-% \frac{1}{2}}\sum_{s=0}^{\infty}(-1)^{s}\frac{{\left(\frac{1}{2}+a\right)_{2s}}% }{s!(2z^{2})^{s}},}}
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    DLMF id
    DLMF:12.9.E1
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    constraint
    | ph ⁡ z | ≤ 3 4 ⁢ π - δ ( < 3 4 ⁢ π ) phase 𝑧 annotated 3 4 𝜋 𝛿 absent 3 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{4}\pi-\delta(<% \tfrac{3}{4}\pi)}}
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    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
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