DLMF:12.14.E23 (Q4263)

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DLMF:12.14.E23
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    Statements

    Defining formula
    s 1 ⁢ ( a , x ) + i ⁢ s 2 ⁢ ( a , x ) ∼ ∑ r = 0 ∞ ( - i ) r ⁢ ( 1 2 + i ⁢ a ) 2 ⁢ r 2 r ⁢ r ! ⁢ x 2 ⁢ r . asymptotic-expansion subscript 𝑠 1 𝑎 𝑥 𝑖 subscript 𝑠 2 𝑎 𝑥 superscript subscript 𝑟 0 superscript 𝑖 𝑟 Pochhammer 1 2 𝑖 𝑎 2 𝑟 superscript 2 𝑟 𝑟 superscript 𝑥 2 𝑟 {\displaystyle{\displaystyle s_{1}(a,x)+is_{2}(a,x)\sim\sum_{r=0}^{\infty}(-i)% ^{r}\frac{{\left(\tfrac{1}{2}+ia\right)_{2r}}}{2^{r}r!x^{2r}}.}}
    0 references
    DLMF id
    DLMF:12.14.E23
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
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