Formula:709

Digital Library of Mathematical Functions ID 2.3.E20

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{ixt}q(t)\mathrm{d}t\sim\sum_{s=0}^{\infty}\exp\left(\frac{(s+\lambda)\pi i}{2\mu}\right)\Gamma\left(\frac{s+\lambda}{\mu}\right)\frac{a_{s}}{x^{(s+\lambda)/\mu}},}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle q(t)}}$: function (locally)
• ${\displaystyle{\displaystyle a_{s}}}$: positive constant
• ${\displaystyle{\displaystyle\lambda}}$: positive constant
• ${\displaystyle{\displaystyle\mu}}$: positive constant
 

Resources that cite this formula

No records found.