Formula:809

Digital Library of Mathematical Functions ID 2.6.E14

${\displaystyle{\displaystyle\left\langle t^{-s-1},\phi\right\rangle=-\frac{1}{s!}\int_{0}^{\infty}(\ln t)\phi^{(s+1)}(t)\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle\phi\in\mathcal{T}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right\rangle}}$:
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\mathcal{T}}}$: space of decreasing functions
 

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