DLMF:3.5.E42 (Q1298): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aodec
Property / Symbols used
 
Property / Symbols used: Q11176 / rank
 
Normal rank
Property / Symbols used: Q11176 / qualifier
 
test:

λ 𝜆 {\displaystyle{\displaystyle\lambda}}

\lambda
Property / Symbols used: Q11176 / qualifier
 
xml-id: C3.S5.XMD21.m1dec

Latest revision as of 16:52, 1 January 2020

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DLMF:3.5.E42
No description defined

    Statements

    test
    erfc ⁡ λ = 1 2 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ e ζ - 2 ⁢ λ ⁢ ζ ⁢ d ζ ζ , complementary-error-function 𝜆 1 2 imaginary-unit superscript subscript 𝑐 imaginary-unit 𝑐 imaginary-unit superscript 𝑒 𝜁 2 𝜆 𝜁 𝜁 𝜁 {\displaystyle{\displaystyle\operatorname{erfc}\lambda=\frac{1}{2\pi\mathrm{i}% }\int_{c-\mathrm{i}\infty}^{c+\mathrm{i}\infty}e^{\zeta-2\lambda\sqrt{\zeta}}% \frac{\mathrm{d}\zeta}{\zeta},}}
    0 references
    DLMF id
    DLMF:3.5.E42
    0 references
    constraint
    c > 0 𝑐 0 {\displaystyle{\displaystyle c>0}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    complementary error function
    test
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2adec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2agdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aodec
    0 references
    Q11176
    test
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C3.S5.XMD21.m1dec
    0 references
     
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