DLMF:3.5.E45 (Q1301): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aqdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ajdec
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.m3aqdec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
test:

tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2adec
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.m1cdec

Latest revision as of 16:53, 1 January 2020

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DLMF:3.5.E45
No description defined

    Statements

    test
    erfc ⁡ λ = e - λ 2 2 ⁢ π ⁢ ∫ - π π e - λ 2 ⁢ tan 2 ⁡ ( 1 2 ⁢ θ ) ⁢ d θ . complementary-error-function 𝜆 superscript 𝑒 superscript 𝜆 2 2 superscript subscript superscript 𝑒 superscript 𝜆 2 2 1 2 𝜃 𝜃 {\displaystyle{\displaystyle\operatorname{erfc}\lambda=\frac{e^{-\lambda^{2}}}% {2\pi}\int_{-\pi}^{\pi}e^{-\lambda^{2}{\tan^{2}}\left(\frac{1}{2}\theta\right)% }\mathrm{d}\theta.}}
    0 references
    DLMF id
    DLMF:3.5.E45
    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.m2akdec
    0 references
    complementary error function
    test
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aqdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aqdec
    0 references
    tangent function
    test
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2adec
    0 references
    Q11176
    test
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C3.S5.XMD21.m1cdec
    0 references
     
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