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DLMF:12.14.E4 - MaRDI portal

DLMF:12.14.E4 (Q4936)

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DLMF:12.14.E4
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    Statements

    DLMF defining formula
    W ⁡ ( a , x ) = k / 2 ⁢ e 1 4 ⁢ π ⁢ a ⁢ ( e i ⁢ ρ ⁢ U ⁡ ( i ⁢ a , x ⁢ e - π ⁢ i / 4 ) + e - i ⁢ ρ ⁢ U ⁡ ( - i ⁢ a , x ⁢ e π ⁢ i / 4 ) ) , parabolic-W 𝑎 𝑥 𝑘 2 superscript 𝑒 1 4 𝜋 𝑎 superscript 𝑒 𝑖 𝜌 parabolic-U 𝑖 𝑎 𝑥 superscript 𝑒 𝜋 𝑖 4 superscript 𝑒 𝑖 𝜌 parabolic-U 𝑖 𝑎 𝑥 superscript 𝑒 𝜋 𝑖 4 {\displaystyle{\displaystyle W\left(a,x\right)=\sqrt{k/2}\,e^{\frac{1}{4}\pi a% }\left(e^{i\rho}U\left(ia,xe^{-\pi i/4}\right)+e^{-i\rho}U\left(-ia,xe^{\pi i/% 4}\right)\right),}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11291
    DLMF defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1adec
    0 references
    Q11514
    DLMF defining formula
    W ⁡ ( a , x ) parabolic-W 𝑎 𝑥 {\displaystyle{\displaystyle W\left(\NVar{a},\NVar{x}\right)}}
    xml-id
    C12.S14.SS1.p1.m1agdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C12.S1.XMD1.m1edec
    0 references
    real or complex parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1cdec
    0 references
    k
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C12.S14.XMD1.m1ddec
    0 references
    12.14.E6
    DLMF defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C12.S14.XMD2.m1dec
    0 references

    Identifiers

     
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