DLMF:7.7.E7 (Q2377)

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DLMF:7.7.E7
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    Statements

    Defining formula
    ∫ x ∞ e - a 2 ⁢ t 2 - ( b 2 / t 2 ) ⁢ d t = π 4 ⁢ a ⁢ ( e 2 ⁢ a ⁢ b ⁢ erfc ⁡ ( a ⁢ x + ( b / x ) ) + e - 2 ⁢ a ⁢ b ⁢ erfc ⁡ ( a ⁢ x - ( b / x ) ) ) , superscript subscript 𝑥 superscript 𝑒 superscript 𝑎 2 superscript 𝑡 2 superscript 𝑏 2 superscript 𝑡 2 𝑡 𝜋 4 𝑎 superscript 𝑒 2 𝑎 𝑏 complementary-error-function 𝑎 𝑥 𝑏 𝑥 superscript 𝑒 2 𝑎 𝑏 complementary-error-function 𝑎 𝑥 𝑏 𝑥 {\displaystyle{\displaystyle\int_{x}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}% \mathrm{d}t=\frac{\sqrt{\pi}}{4a}\left(e^{2ab}\operatorname{erfc}\left(ax+(b/x% )\right)+e^{-2ab}\operatorname{erfc}\left(ax-(b/x)\right)\right),}}
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    DLMF id
    DLMF:7.7.E7
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    constraint
    | ph ⁡ a | < 1 4 ⁢ π phase 𝑎 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}
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    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
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    | ph ⁡ a | < 1 4 ⁢ π ph 𝑎 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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