DLMF:7.14.E4 (Q2436)

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DLMF:7.14.E4
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    Statements

    Defining formula
    ∫ 0 ∞ e ( a - b ) ⁢ t ⁢ erfc ⁡ ( a ⁢ t + c t ) ⁢ d t = e - 2 ⁢ ( a ⁢ c + b ⁢ c ) b ⁢ ( a + b ) , superscript subscript 0 superscript 𝑒 𝑎 𝑏 𝑡 complementary-error-function 𝑎 𝑡 𝑐 𝑡 𝑡 superscript 𝑒 2 𝑎 𝑐 𝑏 𝑐 𝑏 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{(a-b)t}\operatorname{erfc}% \left(\sqrt{at}+\sqrt{\frac{c}{t}}\right)\mathrm{d}t=\frac{e^{-2(\sqrt{ac}+% \sqrt{bc})}}{\sqrt{b}(\sqrt{a}+\sqrt{b})},}}
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    DLMF id
    DLMF:7.14.E4
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    constraint
    | ph ⁡ a | < 1 2 ⁢ π phase 𝑎 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}a|<\frac{1}{2}\pi}}
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    ℜ ⁡ b > 0 𝑏 0 {\displaystyle{\displaystyle\Re b>0}}
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    ℜ ⁡ c ≥ 0 𝑐 0 {\displaystyle{\displaystyle\Re c\geq 0}}
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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.m2abdec
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