DLMF:1.14.E35 (Q527): 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.m2aldec
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.m1axdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2agdec
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.m3awdec
Property / Symbols used
 
Property / Symbols used: Q10894 / rank
 
Normal rank
Property / Symbols used: Q10894 / qualifier
 
test:

σ ( a , b ) 𝜎 𝑎 𝑏 {\displaystyle{\displaystyle\sigma\in(a,b)}}

\sigma\in(a,b)
Property / Symbols used: Q10894 / qualifier
 
xml-id: C1.S14.XMD11.m1cdec

Latest revision as of 15:26, 1 January 2020

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DLMF:1.14.E35
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    Statements

    f ( x ) = 1 2 π i σ - i σ + i x - s f ( s ) d s . 𝑓 𝑥 1 2 𝜋 𝑖 subscript superscript 𝜎 𝑖 𝜎 𝑖 superscript 𝑥 𝑠 Mellin-transform 𝑓 𝑠 𝑠 {\displaystyle{\displaystyle f(x)=\frac{1}{2\pi i}\int^{\sigma+i\infty}_{% \sigma-i\infty}x^{-s}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(s\right)% \mathrm{d}s.}}
    0 references
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    ( f ) ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    C1.S14.E32.m2acdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aldec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1axdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2agdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3awdec
    0 references
    σ ( a , b ) 𝜎 𝑎 𝑏 {\displaystyle{\displaystyle\sigma\in(a,b)}}
    C1.S14.XMD11.m1cdec
    0 references