DLMF:2.5.E40 (Q816): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
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.m2ahdec

Revision as of 16:06, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.5.E40
No description defined

    Statements

    test
    I j ⁢ ( x ) = 1 2 ⁢ π ⁢ i ⁢ ∫ p j - i ⁢ ∞ p j + i ⁢ ∞ x - z ⁢ Γ ⁡ ( 1 - z ) ⁢ ℳ ⁡ h j ⁡ ( z ) ⁢ d z , subscript 𝐼 𝑗 𝑥 1 2 𝜋 𝑖 superscript subscript subscript 𝑝 𝑗 𝑖 subscript 𝑝 𝑗 𝑖 superscript 𝑥 𝑧 Euler-Gamma 1 𝑧 Mellin-transform subscript ℎ 𝑗 𝑧 𝑧 {\displaystyle{\displaystyle I_{j}(x)=\frac{1}{2\pi i}\int_{p_{j}-i\infty}^{p_% {j}+i\infty}x^{-z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{j}\mskip 3.% 0mu \left(z\right)\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:2.5.E40
    0 references
    constraint
    j = 1 , 2 𝑗 1 2 {\displaystyle{\displaystyle j=1,2}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    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.m2andec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q816&oldid=4501"