DLMF:2.5.E10 (Q786): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1abdec

Revision as of 16:02, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.5.E10
No description defined

    Statements

    test
    ℳ ⁡ h ⁡ ( z ) = 2 z - 1 ⁢ Γ ⁡ ( ν + 1 2 ⁢ z ) Γ 2 ⁡ ( 1 - 1 2 ⁢ z ) ⁢ Γ ⁡ ( 1 + ν - 1 2 ⁢ z ) ⁢ Γ ⁡ ( z ) ⁢ π sin ⁡ ( π ⁢ z ) , Mellin-transform ℎ 𝑧 superscript 2 𝑧 1 Euler-Gamma 𝜈 1 2 𝑧 Euler-Gamma 2 1 1 2 𝑧 Euler-Gamma 1 𝜈 1 2 𝑧 Euler-Gamma 𝑧 𝜋 𝜋 𝑧 {\displaystyle{\displaystyle\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z% \right)=\frac{2^{z-1}\Gamma\left(\nu+\frac{1}{2}z\right)}{{\Gamma^{2}}\left(1-% \frac{1}{2}z\right)\Gamma\left(1+\nu-\frac{1}{2}z\right)\Gamma\left(z\right)}% \frac{\pi}{\sin\left(\pi z\right)},}}
    0 references
    DLMF id
    DLMF:2.5.E10
    0 references
    constraint
    - 2 ⁢ ν < ℜ ⁡ z < 1 2 𝜈 𝑧 1 {\displaystyle{\displaystyle-2\nu<\Re z<1}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    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.m2agdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q786&oldid=4344"