DLMF:4.10.E11 (Q1626): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ajdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2acdec
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.m3aidec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11230 / rank
 
Normal rank
Property / Symbols used: Q11230 / qualifier
 
Defining formula:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11230 / qualifier
 
xml-id: C4.S1.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1adec

Latest revision as of 18:15, 1 January 2020

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Language Label Description Also known as
English
DLMF:4.10.E11
No description defined

    Statements

    Defining formula
    ∫ - ∞ ∞ e - c ⁢ x 2 ⁢ d x = π c , superscript subscript superscript 𝑒 𝑐 superscript 𝑥 2 𝑥 𝜋 𝑐 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}e^{-cx^{2}}\mathrm{d}x=% \sqrt{\frac{\pi}{c}},}}
    0 references
    DLMF id
    DLMF:4.10.E11
    0 references
    constraint
    ℜ ⁡ c > 0 𝑐 0 {\displaystyle{\displaystyle\Re c>0}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q11230
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C4.S1.XMD5.m1dec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1adec
    0 references
     
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