DLMF:8.4.E14 (Q2508)

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DLMF:8.4.E14
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    Statements

    Defining formula
    Q ⁡ ( n + 1 2 , z 2 ) = erfc ⁡ ( z ) + e - z 2 π ⁢ ∑ k = 1 n z 2 ⁢ k - 1 ( 1 2 ) k , incomplete-gamma-Q 𝑛 1 2 superscript 𝑧 2 complementary-error-function 𝑧 superscript 𝑒 superscript 𝑧 2 𝜋 superscript subscript 𝑘 1 𝑛 superscript 𝑧 2 𝑘 1 Pochhammer 1 2 𝑘 {\displaystyle{\displaystyle Q\left(n+\tfrac{1}{2},z^{2}\right)=\operatorname{% erfc}\left(z\right)+\frac{e^{-z^{2}}}{\sqrt{\pi}}\sum_{k=1}^{n}\frac{z^{2k-1}}% {{\left(\tfrac{1}{2}\right)_{k}}},}}
    0 references
    DLMF id
    DLMF:8.4.E14
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    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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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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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.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
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    Q11326
    Defining formula
    Q ⁡ ( a , z ) incomplete-gamma-Q 𝑎 𝑧 {\displaystyle{\displaystyle Q\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E4.m2aadec
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    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1ldec
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    Q11330
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1adec
    0 references
     
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