Formula:698

Digital Library of Mathematical Functions ID 2.3.E12

${\displaystyle{\displaystyle\int_{0}^{\infty}f(xt)q(t)\mathrm{d}t\sim\sum_{s=0}^{\infty}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(\frac{s+\lambda}{\mu}\right)\frac{a_{s}}{x^{(s+\lambda)/\mu}},}}$

Constraint(s)

${\displaystyle{\displaystyle x\to+\infty}}$

Symbols List

• ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Mellin transform
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle f(x)}}$: function
• ${\displaystyle{\displaystyle a}}$: positive constant
• ${\displaystyle{\displaystyle q(t)}}$: function (locally)
• ${\displaystyle{\displaystyle\lambda}}$: positive constant
• ${\displaystyle{\displaystyle\mu}}$: positive constant
 

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