DLMF:7.14.E3 (Q2435)

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DLMF:7.14.E3
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ erf ⁡ b ⁢ t ⁢ d t = 1 a ⁢ b a + b , superscript subscript 0 superscript 𝑒 𝑎 𝑡 error-function 𝑏 𝑡 𝑡 1 𝑎 𝑏 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\operatorname{erf}\sqrt{bt% }\mathrm{d}t=\frac{1}{a}\sqrt{\frac{b}{a+b}},}}
    0 references
    DLMF id
    DLMF:7.14.E3
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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    ℜ ⁡ b > 0 𝑏 0 {\displaystyle{\displaystyle\Re b>0}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    error function
    Defining formula
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
     
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