DLMF:2.5.E44 (Q820): Difference between revisions

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ζ 0 + 𝜁 limit-from 0 {\displaystyle{\displaystyle\zeta\to 0+}}

\zeta\to 0+
Property / constraint: ζ 0 + 𝜁 limit-from 0 {\displaystyle{\displaystyle\zeta\to 0+}} / rank
 
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Revision as of 16:53, 30 December 2019

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DLMF:2.5.E44
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    h ( ζ ) n = 0 b n Γ ( 1 - β n ) ζ β n - 1 + n = 0 ( - ζ ) n n ! h ( n + 1 ) , asymptotic-expansion Laplace-transform 𝜁 superscript subscript 𝑛 0 subscript 𝑏 𝑛 Euler-Gamma 1 subscript 𝛽 𝑛 superscript 𝜁 subscript 𝛽 𝑛 1 superscript subscript 𝑛 0 superscript 𝜁 𝑛 𝑛 Mellin-transform 𝑛 1 {\displaystyle{\displaystyle\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta% \right)\sim\sum_{n=0}^{\infty}b_{n}\Gamma\left(1-\beta_{n}\right)\zeta^{\beta_% {n}-1}+\sum\limits_{n=0}^{\infty}\frac{(-\zeta)^{n}}{n!}\mathscr{M}\mskip-3.0% mu h\mskip 3.0mu \left(n+1\right),}}
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    DLMF:2.5.E44
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    ζ 0 + 𝜁 limit-from 0 {\displaystyle{\displaystyle\zeta\to 0+}}
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