DLMF:12.7.E5 (Q4128)

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DLMF:12.7.E5
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    Statements

    Defining formula
    U ⁡ ( 1 2 , z ) = D - 1 ⁡ ( z ) = 1 2 ⁢ π ⁢ e 1 4 ⁢ z 2 ⁢ erfc ⁡ ( z / 2 ) , parabolic-U 1 2 𝑧 Whittaker-D 1 𝑧 1 2 𝜋 superscript 𝑒 1 4 superscript 𝑧 2 complementary-error-function 𝑧 2 {\displaystyle{\displaystyle U\left(\tfrac{1}{2},z\right)=D_{-1}\left(z\right)% =\sqrt{\tfrac{1}{2}\pi}\,e^{\frac{1}{4}z^{2}}\operatorname{erfc}\left(z/\sqrt{% 2}\right),}}
    0 references
    DLMF id
    DLMF:12.7.E5
    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.m6abdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    complementary error function
    Defining formula
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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    Q11320
    Defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1abdec
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    Q11513
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C12.S1.XMD3.m1ddec
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