DLMF:2.4.E14 (Q768): Difference between revisions

From DRMF
Jump to navigation Jump to search
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
(7 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.m2ajdec
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: Q10972 / rank
 
Normal rank
Property / Symbols used: Q10972 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q10972 / qualifier
 
xml-id: C2.S4.XMD11.m1edec
Property / Symbols used
 
Property / Symbols used: Q10980 / rank
 
Normal rank
Property / Symbols used: Q10980 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q10980 / qualifier
 
xml-id: C2.S4.XMD12.m1bdec
Property / Symbols used
 
Property / Symbols used: contour integral (locally) / rank
 
Normal rank
Property / Symbols used: contour integral (locally) / qualifier
 
Defining formula:

I ⁢ ( z ) 𝐼 𝑧 {\displaystyle{\displaystyle I(z)}}

I(z)
Property / Symbols used: contour integral (locally) / qualifier
 
xml-id: C2.S4.XMD13.m1bdec
Property / Symbols used
 
Property / Symbols used: Q10981 / rank
 
Normal rank
Property / Symbols used: Q10981 / qualifier
 
Defining formula:

p ⁢ ( t ) 𝑝 𝑡 {\displaystyle{\displaystyle p(t)}}

p(t)
Property / Symbols used: Q10981 / qualifier
 
xml-id: C2.S4.XMD15.m1cdec
Property / Symbols used
 
Property / Symbols used: Q10973 / rank
 
Normal rank
Property / Symbols used: Q10973 / qualifier
 
Defining formula:

q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}

q(t)
Property / Symbols used: Q10973 / qualifier
 
xml-id: C2.S4.XMD16.m1idec

Latest revision as of 16:59, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.4.E14
No description defined

    Statements

    Defining formula
    I ⁢ ( z ) = ∫ t 0 b e - z ⁢ p ⁢ ( t ) ⁢ q ⁢ ( t ) ⁢ d t - ∫ t 0 a e - z ⁢ p ⁢ ( t ) ⁢ q ⁢ ( t ) ⁢ d t , 𝐼 𝑧 superscript subscript subscript 𝑡 0 𝑏 superscript 𝑒 𝑧 𝑝 𝑡 𝑞 𝑡 𝑡 superscript subscript subscript 𝑡 0 𝑎 superscript 𝑒 𝑧 𝑝 𝑡 𝑞 𝑡 𝑡 {\displaystyle{\displaystyle I(z)=\int_{t_{0}}^{b}e^{-zp(t)}q(t)\mathrm{d}t-% \int_{t_{0}}^{a}e^{-zp(t)}q(t)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:2.4.E14
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    Q10972
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C2.S4.XMD11.m1edec
    0 references
    Q10980
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C2.S4.XMD12.m1bdec
    0 references
    contour integral (locally)
    Defining formula
    I ⁢ ( z ) 𝐼 𝑧 {\displaystyle{\displaystyle I(z)}}
    xml-id
    C2.S4.XMD13.m1bdec
    0 references
    Q10981
    Defining formula
    p ⁢ ( t ) 𝑝 𝑡 {\displaystyle{\displaystyle p(t)}}
    xml-id
    C2.S4.XMD15.m1cdec
    0 references
    Q10973
    Defining formula
    q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}
    xml-id
    C2.S4.XMD16.m1idec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q768&oldid=24334"