DLMF:7.7.E8 (Q2378): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m1agdec
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.m2agdec
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.m3agdec
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.m1abdec

Latest revision as of 01:44, 2 January 2020

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DLMF:7.7.E8
No description defined

    Statements

    0 e - a 2 t 2 - ( b 2 / t 2 ) d t = π 2 a e - 2 a b , superscript subscript 0 superscript 𝑒 superscript 𝑎 2 superscript 𝑡 2 superscript 𝑏 2 superscript 𝑡 2 𝑡 𝜋 2 𝑎 superscript 𝑒 2 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}% \mathrm{d}t=\frac{\sqrt{\pi}}{2a}e^{-2ab},}}
    0 references
    DLMF:7.7.E8
    0 references
    | ph a | < 1 4 π phase 𝑎 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}
    0 references
    | ph b | < 1 4 π phase 𝑏 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}b|<\tfrac{1}{4}\pi}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2agdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1agdec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2agdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3agdec
    0 references
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1abdec
    0 references