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

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Property / Symbols used
 
Property / Symbols used: Q10992 / rank
 
Normal rank
Property / Symbols used: Q10992 / qualifier
 
Defining formula:

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

f(x)
Property / Symbols used: Q10992 / qualifier
 
xml-id: C2.S5.XMD1.m1edec
Property / Symbols used
 
Property / Symbols used: Q10993 / rank
 
Normal rank
Property / Symbols used: Q10993 / qualifier
 
Defining formula:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q10993 / qualifier
 
xml-id: C2.S5.XMD4.m1bdec
Property / Symbols used
 
Property / Symbols used: Q10994 / rank
 
Normal rank
Property / Symbols used: Q10994 / qualifier
 
Defining formula:

I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}

I(x)
Property / Symbols used: Q10994 / qualifier
 
xml-id: C2.S5.XMD5.m1cdec
Property / Symbols used
 
Property / Symbols used: Q10995 / rank
 
Normal rank
Property / Symbols used: Q10995 / qualifier
 
Defining formula:

h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}

h(x)
Property / Symbols used: Q10995 / qualifier
 
xml-id: C2.S5.XMD6.m1cdec
Property / Symbols used
 
Property / Symbols used: Q10996 / rank
 
Normal rank
Property / Symbols used: Q10996 / qualifier
 
Defining formula:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q10996 / qualifier
 
xml-id: C2.S5.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: Q10997 / rank
 
Normal rank
Property / Symbols used: Q10997 / qualifier
 
Defining formula:

E ⁢ ( x ) 𝐸 𝑥 {\displaystyle{\displaystyle E(x)}}

E(x)
Property / Symbols used: Q10997 / qualifier
 
xml-id: C2.S5.XMD8.m1dec

Latest revision as of 17:02, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.5.E6
No description defined

    Statements

    Defining formula
    I ⁢ ( x ) = ∑ d < ℜ ⁡ z < c res ⁡ [ x - z ⁢ ℳ ⁡ f ⁡ ( 1 - z ) ⁢ ℳ ⁡ h ⁡ ( z ) ] + E ⁢ ( x ) , 𝐼 𝑥 subscript 𝑑 𝑧 𝑐 residue delimited-[] superscript 𝑥 𝑧 Mellin-transform 𝑓 1 𝑧 Mellin-transform ℎ 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),}}
    0 references
    DLMF id
    DLMF:2.5.E6
    0 references
    Symbols used
    Mellin transform
    Defining formula
    ℳ ⁡ ( f ) ⁡ ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E32.m2addec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q10960
    Defining formula
    res residue {\displaystyle{\displaystyle\Residue}}
    xml-id
    C1.S10.SS3.p5.m4adec
    0 references
    Q10992
    Defining formula
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S5.XMD1.m1edec
    0 references
    Q10993
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C2.S5.XMD4.m1bdec
    0 references
    Q10994
    Defining formula
    I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}
    xml-id
    C2.S5.XMD5.m1cdec
    0 references
    Q10995
    Defining formula
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S5.XMD6.m1cdec
    0 references
    Q10996
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C2.S5.XMD7.m1dec
    0 references
    Q10997
    Defining formula
    E ⁢ ( x ) 𝐸 𝑥 {\displaystyle{\displaystyle E(x)}}
    xml-id
    C2.S5.XMD8.m1dec
    0 references
     
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