DLMF:2.5.E7 (Q783): Difference between revisions

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imported>Admin
 
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Property / Symbols used
 
Property / Symbols used: Mellin transform / rank
 
Normal rank
Property / Symbols used: Mellin transform / qualifier
 
test:

ℳ ⁡ ( f ) ⁡ ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}

\Mellintrans@{\NVar{f}}@{\NVar{s}}
Property / Symbols used: Mellin transform / qualifier
 
xml-id: C1.S14.E32.m2aedec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1addec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3addec
Property / Symbols used
 
Property / Symbols used: Q10992 / rank
 
Normal rank
Property / Symbols used: Q10992 / qualifier
 
test:

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

f(x)
Property / Symbols used: Q10992 / qualifier
 
xml-id: C2.S5.XMD1.m1fdec
Property / Symbols used
 
Property / Symbols used: Q10995 / rank
 
Normal rank
Property / Symbols used: Q10995 / qualifier
 
test:

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

h(x)
Property / Symbols used: Q10995 / qualifier
 
xml-id: C2.S5.XMD6.m1ddec
Property / Symbols used
 
Property / Symbols used: Q10996 / rank
 
Normal rank
Property / Symbols used: Q10996 / qualifier
 
test:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q10996 / qualifier
 
xml-id: C2.S5.XMD7.m1adec
Property / Symbols used
 
Property / Symbols used: Q10997 / rank
 
Normal rank
Property / Symbols used: Q10997 / qualifier
 
test:

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

E(x)
Property / Symbols used: Q10997 / qualifier
 
xml-id: C2.S5.XMD8.m1adec

Latest revision as of 16:02, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.5.E7
No description defined

    Statements

    test
    E ⁢ ( x ) = 1 2 ⁢ π ⁢ i ⁢ ∫ d - i ⁢ ∞ d + i ⁢ ∞ x - z ⁢ ℳ ⁡ f ⁡ ( 1 - z ) ⁢ ℳ ⁡ h ⁡ ( z ) ⁢ d z . 𝐸 𝑥 1 2 𝜋 𝑖 superscript subscript 𝑑 𝑖 𝑑 𝑖 superscript 𝑥 𝑧 Mellin-transform 𝑓 1 𝑧 Mellin-transform ℎ 𝑧 𝑧 {\displaystyle{\displaystyle E(x)=\frac{1}{2\pi i}\int_{d-i\infty}^{d+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 id
    DLMF:2.5.E7
    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.m2aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q10992
    test
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S5.XMD1.m1fdec
    0 references
    Q10995
    test
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S5.XMD6.m1ddec
    0 references
    Q10996
    test
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C2.S5.XMD7.m1adec
    0 references
    Q10997
    test
    E ⁢ ( x ) 𝐸 𝑥 {\displaystyle{\displaystyle E(x)}}
    xml-id
    C2.S5.XMD8.m1adec
    0 references
     
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