DLMF:2.6.E62 (Q888)

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DLMF:2.6.E62
No description defined

    Statements

    Defining formula
    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
    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.m2afdec
    0 references
    Q11019
    Defining formula
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1agdec
    0 references
    Q11037
    Defining formula
    I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}
    xml-id
    C2.S6.XMD26.m1adec
    0 references
    Q11039
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD27.m1ddec
    0 references
    Q11040
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S6.XMD28.m1bdec
    0 references
    Q11041
    Defining formula
    b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}}
    xml-id
    C2.S6.XMD29.m1bdec
    0 references
    Q11038
    Defining formula
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S6.XMD30.m1ddec
    0 references
    Q11042
    Defining formula
    δ n ⁢ ( x ) subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)}}
    xml-id
    C2.S6.XMD31.m1dec
    0 references
     
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