DLMF:2.6.E21 (Q846): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11025 / rank
 
Normal rank
Property / Symbols used: Q11025 / qualifier
 
test:

d s subscript 𝑑 𝑠 {\displaystyle{\displaystyle d_{s}}}

d_{s}
Property / Symbols used: Q11025 / qualifier
 
xml-id: C2.S6.XMD10.m1adec
Property / Symbols used
 
Property / Symbols used: Q11019 / rank
 
Normal rank
Property / Symbols used: Q11019 / qualifier
 
test:

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

f(t)
Property / Symbols used: Q11019 / qualifier
 
xml-id: C2.S6.XMD2.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11020 / rank
 
Normal rank
Property / Symbols used: Q11020 / qualifier
 
test:

a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}

a_{n}
Property / Symbols used: Q11020 / qualifier
 
xml-id: C2.S6.XMD3.m1ddec

Latest revision as of 16:12, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.6.E21
No description defined

    Statements

    test
    ( - 1 ) s + 1 ⁢ d s + 1 = a s s ! ⁢ ∑ k = 1 s 1 k + 1 s ! ⁢ lim z → s + 1 ⁡ ( ℳ ⁡ f ⁡ ( z ) + a s z - s - 1 ) , superscript 1 𝑠 1 subscript 𝑑 𝑠 1 subscript 𝑎 𝑠 𝑠 superscript subscript 𝑘 1 𝑠 1 𝑘 1 𝑠 subscript → 𝑧 𝑠 1 Mellin-transform 𝑓 𝑧 subscript 𝑎 𝑠 𝑧 𝑠 1 {\displaystyle{\displaystyle(-1)^{s+1}d_{s+1}=\frac{a_{s}}{s!}\sum_{k=1}^{s}% \frac{1}{k}+\frac{1}{s!}\lim_{z\to s+1}\left(\mathscr{M}\mskip-3.0mu f\mskip 3% .0mu \left(z\right)+\frac{a_{s}}{z-s-1}\right),}}
    0 references
    DLMF id
    DLMF:2.6.E21
    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.m2aadec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
    0 references
    Q11025
    test
    d s subscript 𝑑 𝑠 {\displaystyle{\displaystyle d_{s}}}
    xml-id
    C2.S6.XMD10.m1adec
    0 references
    Q11019
    test
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1gdec
    0 references
    Q11020
    test
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S6.XMD3.m1ddec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q846&oldid=4713"