DLMF:1.14.E37 (Q529): 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.m2andec

Revision as of 15:26, 1 January 2020

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DLMF:1.14.E37
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    Statements

    test
    ∫ 0 ∞ f ⁢ ( x ) ⁢ g ⁢ ( x ) ⁢ d x = 1 2 ⁢ π ⁢ i ⁢ ∫ σ - i ⁢ ∞ σ + i ⁢ ∞ ℳ ⁡ f ⁡ ( 1 - s ) ⁢ ℳ ⁡ g ⁡ ( s ) ⁢ d s . subscript superscript 0 𝑓 𝑥 𝑔 𝑥 𝑥 1 2 𝜋 𝑖 subscript superscript 𝜎 𝑖 𝜎 𝑖 Mellin-transform 𝑓 1 𝑠 Mellin-transform 𝑔 𝑠 𝑠 {\displaystyle{\displaystyle\int^{\infty}_{0}f(x)g(x)\mathrm{d}x=\frac{1}{2\pi i% }\*\int^{\sigma+i\infty}_{\sigma-i\infty}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu% \left(1-s\right)\mathscr{M}\mskip-3.0mu g\mskip 3.0mu \left(s\right)\mathrm{d% }s.}}
    0 references
    DLMF id
    DLMF:1.14.E37
    0 references
    Symbols used
    Mellin transform
    test
    ℳ ⁡ ( f ) ⁡ ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E32.m2aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2andec
    0 references
     
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