DLMF:7.7.E1 (Q2371): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec
Property / Symbols used
 
Property / Symbols used: Q11312 / rank
 
Normal rank
Property / Symbols used: Q11312 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11312 / qualifier
 
xml-id: C7.S1.XMD2.m1dec

Latest revision as of 01:43, 2 January 2020

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DLMF:7.7.E1
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    Statements

    erfc z = 2 π e - z 2 0 e - z 2 t 2 t 2 + 1 d t , complementary-error-function 𝑧 2 𝜋 superscript 𝑒 superscript 𝑧 2 superscript subscript 0 superscript 𝑒 superscript 𝑧 2 superscript 𝑡 2 superscript 𝑡 2 1 𝑡 {\displaystyle{\displaystyle\operatorname{erfc}z=\frac{2}{\pi}e^{-z^{2}}\int_{% 0}^{\infty}\frac{e^{-z^{2}t^{2}}}{t^{2}+1}\mathrm{d}t,}}
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    DLMF:7.7.E1
    0 references
    | ph z | 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\pi}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    erfc z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    C7.S2.E2.m2adec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
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    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C7.S1.XMD2.m1dec
    0 references