DLMF:2.5.E5 (Q781): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3acdec
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.m1ddec
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.m1adec
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.m1bdec
Property / Symbols used
 
Property / Symbols used: Q10995 / rank
 
Normal rank
Property / Symbols used: Q10995 / qualifier
 
Defining formula:

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

h(x)
Property / Symbols used: Q10995 / qualifier
 
xml-id: C2.S5.XMD6.m1bdec

Latest revision as of 17:01, 1 January 2020

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DLMF:2.5.E5
No description defined

    Statements

    I ( x ) = 1 2 π i c - i c + i x - z f ( 1 - z ) h ( z ) d z , 𝐼 𝑥 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 superscript 𝑥 𝑧 Mellin-transform 𝑓 1 𝑧 Mellin-transform 𝑧 𝑧 {\displaystyle{\displaystyle I(x)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}% 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)\mathrm{d}z,}}
    0 references
    DLMF:2.5.E5
    0 references
    ( f ) ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    C1.S14.E32.m2acdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1acdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3acdec
    0 references
    f ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    C2.S5.XMD1.m1ddec
    0 references
    c 𝑐 {\displaystyle{\displaystyle c}}
    C2.S5.XMD4.m1adec
    0 references
    I ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}
    C2.S5.XMD5.m1bdec
    0 references
    h ( x ) 𝑥 {\displaystyle{\displaystyle h(x)}}
    C2.S5.XMD6.m1bdec
    0 references