DLMF:12.14.E37 (Q4279)

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DLMF:12.14.E37
No description defined

    Statements

    Defining formula
    k - 1 / 2 ⁢ W ⁡ ( a , x ) + i ⁢ k 1 / 2 ⁢ W ⁡ ( a , - x ) = F ~ ⁢ ( a , x ) ⁢ e i ⁢ θ ~ ⁢ ( a , x ) , superscript 𝑘 1 2 parabolic-W 𝑎 𝑥 𝑖 superscript 𝑘 1 2 parabolic-W 𝑎 𝑥 ~ 𝐹 𝑎 𝑥 superscript 𝑒 𝑖 ~ 𝜃 𝑎 𝑥 {\displaystyle{\displaystyle k^{-\ifrac{1}{2}}W\left(a,x\right)+ik^{\ifrac{1}{% 2}}W\left(a,-x\right)=\widetilde{F}(a,x)e^{i\widetilde{\theta}(a,x)},}}
    0 references
    DLMF id
    DLMF:12.14.E37
    0 references
    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aidec
    0 references
    Q11543
    Defining formula
    W ⁡ ( a , x ) parabolic-W 𝑎 𝑥 {\displaystyle{\displaystyle W\left(\NVar{a},\NVar{x}\right)}}
    xml-id
    C12.S14.SS1.p1.m1atdec
    0 references
    Q11520
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C12.S1.XMD1.m1sdec
    0 references
    Q11516
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1tdec
    0 references
    Q11544
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C12.S14.XMD1.m1hdec
    0 references
    Q11549
    Defining formula
    F ~ ⁢ ( a , x ) ~ 𝐹 𝑎 𝑥 {\displaystyle{\displaystyle\widetilde{F}(a,x)}}
    xml-id
    C12.S14.XMD16.m1bdec
    0 references
    Q11550
    Defining formula
    θ ~ ⁢ ( a , x ) ~ 𝜃 𝑎 𝑥 {\displaystyle{\displaystyle\widetilde{\theta}(a,x)}}
    xml-id
    C12.S14.XMD18.m1dec
    0 references
     
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