DLMF:7.7.E7 (Q2377): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2afdec
Property / Symbols used
 
Property / Symbols used: complementary error function / rank
 
Normal rank
Property / Symbols used: complementary error function / qualifier
 
test:

erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}

\erfc@@{\NVar{z}}
Property / Symbols used: complementary error function / qualifier
 
xml-id: C7.S2.E2.m2acdec
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.m1afdec
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.m2afdec
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.m3afdec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

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

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1aadec
Property / Symbols used
 
Property / Symbols used: Q11313 / rank
 
Normal rank
Property / Symbols used: Q11313 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11313 / qualifier
 
xml-id: C7.S1.XMD1.m1adec

Latest revision as of 00:44, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:7.7.E7
No description defined

    Statements

    test
    ∫ x ∞ e - a 2 ⁢ t 2 - ( b 2 / t 2 ) ⁢ d t = π 4 ⁢ a ⁢ ( e 2 ⁢ a ⁢ b ⁢ erfc ⁡ ( a ⁢ x + ( b / x ) ) + e - 2 ⁢ a ⁢ b ⁢ erfc ⁡ ( a ⁢ x - ( b / x ) ) ) , superscript subscript 𝑥 superscript 𝑒 superscript 𝑎 2 superscript 𝑡 2 superscript 𝑏 2 superscript 𝑡 2 𝑡 𝜋 4 𝑎 superscript 𝑒 2 𝑎 𝑏 complementary-error-function 𝑎 𝑥 𝑏 𝑥 superscript 𝑒 2 𝑎 𝑏 complementary-error-function 𝑎 𝑥 𝑏 𝑥 {\displaystyle{\displaystyle\int_{x}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}% \mathrm{d}t=\frac{\sqrt{\pi}}{4a}\left(e^{2ab}\operatorname{erfc}\left(ax+(b/x% )\right)+e^{-2ab}\operatorname{erfc}\left(ax-(b/x)\right)\right),}}
    0 references
    DLMF id
    DLMF:7.7.E7
    0 references
    constraint
    | ph ⁡ a | < 1 4 ⁢ π phase 𝑎 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}
    0 references
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
    0 references
    | ph ⁡ a | < 1 4 ⁢ π ph 𝑎 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}
    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.m2afdec
    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.m1afdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aadec
    0 references
    Q11313
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1adec
    0 references
     
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