DLMF:2.6.E62 (Q888): Difference between revisions

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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.m1agdec
Property / Symbols used
 
Property / Symbols used: Q11037 / rank
 
Normal rank
Property / Symbols used: Q11037 / qualifier
 
test:

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

I(x)
Property / Symbols used: Q11037 / qualifier
 
xml-id: C2.S6.XMD26.m1adec
Property / Symbols used
 
Property / Symbols used: Q11039 / rank
 
Normal rank
Property / Symbols used: Q11039 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11039 / qualifier
 
xml-id: C2.S6.XMD27.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11040 / rank
 
Normal rank
Property / Symbols used: Q11040 / qualifier
 
test:

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

a_{n}
Property / Symbols used: Q11040 / qualifier
 
xml-id: C2.S6.XMD28.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11041 / rank
 
Normal rank
Property / Symbols used: Q11041 / qualifier
 
test:

b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}}

b_{n}
Property / Symbols used: Q11041 / qualifier
 
xml-id: C2.S6.XMD29.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11038 / rank
 
Normal rank
Property / Symbols used: Q11038 / qualifier
 
test:

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

h(x)
Property / Symbols used: Q11038 / qualifier
 
xml-id: C2.S6.XMD30.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11042 / rank
 
Normal rank
Property / Symbols used: Q11042 / qualifier
 
test:

δ n ⁢ ( x ) subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)}}

\delta_{n}(x)
Property / Symbols used: Q11042 / qualifier
 
xml-id: C2.S6.XMD31.m1dec

Latest revision as of 16:20, 1 January 2020

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Language Label Description Also known as
English
DLMF:2.6.E62
No description defined

    Statements

    test
    I ⁢ ( x ) = ∑ j = 0 n - 1 a j ⁢ ℳ ⁡ h ⁡ ( j + α ) ⁢ x - j - α + ∑ k = 0 n - 1 b k ⁢ ℳ ⁡ f ⁡ ( 1 - k - β ) ⁢ x - k - β + δ n ⁢ ( x ) 𝐼 𝑥 superscript subscript 𝑗 0 𝑛 1 subscript 𝑎 𝑗 Mellin-transform ℎ 𝑗 𝛼 superscript 𝑥 𝑗 𝛼 superscript subscript 𝑘 0 𝑛 1 subscript 𝑏 𝑘 Mellin-transform 𝑓 1 𝑘 𝛽 superscript 𝑥 𝑘 𝛽 subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle I(x)=\sum_{j=0}^{n-1}a_{j}\mathscr{M}\mskip-3.0mu% h\mskip 3.0mu \left(j+\alpha\right)x^{-j-\alpha}+\sum_{k=0}^{n-1}b_{k}% \mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-k-\beta\right)x^{-k-\beta}+% \delta_{n}(x)}}
    0 references
    DLMF id
    DLMF:2.6.E62
    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.m2afdec
    0 references
    Q11019
    test
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1agdec
    0 references
    Q11037
    test
    I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}
    xml-id
    C2.S6.XMD26.m1adec
    0 references
    Q11039
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD27.m1ddec
    0 references
    Q11040
    test
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S6.XMD28.m1bdec
    0 references
    Q11041
    test
    b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}}
    xml-id
    C2.S6.XMD29.m1bdec
    0 references
    Q11038
    test
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S6.XMD30.m1ddec
    0 references
    Q11042
    test
    δ n ⁢ ( x ) subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)}}
    xml-id
    C2.S6.XMD31.m1dec
    0 references
     
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