DLMF:2.5.E6 (Q782): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec

Revision as of 17:01, 1 January 2020

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DLMF:2.5.E6
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    Statements

    I ( x ) = d < z < c res [ x - z f ( 1 - z ) h ( z ) ] + E ( x ) , 𝐼 𝑥 subscript 𝑑 𝑧 𝑐 residue delimited-[] superscript 𝑥 𝑧 Mellin-transform 𝑓 1 𝑧 Mellin-transform 𝑧 𝐸 𝑥 {\displaystyle{\displaystyle I(x)=\sum\limits_{d<\Re z<c}\Residue\left[x^{-z}% \mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-3.0mu % h\mskip 3.0mu \left(z\right)\right]+E(x),}}
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    DLMF:2.5.E6
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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.m2addec
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    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
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