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DLMF:7.14.E3 - MaRDI portal

DLMF:7.14.E3 (Q3133)

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DLMF:7.14.E3
No description defined

    Statements

    DLMF 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
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    ℜ ⁡ b > 0 𝑏 0 {\displaystyle{\displaystyle\Re b>0}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    error function
    DLMF defining formula
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2aadec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    real part
    DLMF defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references

    Identifiers

     
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