Why does laplace trancsform of trigonometric functions like tan,sec , cosec,cot,..and logarithmic functions doesnot exist? what is the reason behind that?
pls help friends...
... in general necerssary condition for the existence of the integral...
$\displaystyle \displaystyle \int_{0}^{\infty} f(t)\ e^{-s t}\ dt$ (1)
... is that $\displaystyle f(*)$ is locally integrable on $\displaystyle [0,\infty)$. A function is said to be 'locally integrable' if it is integrable on any compact set of its domain of definition. Functions like $\displaystyle \displaystyle \tan t$, $\displaystyle \displaystyle \frac{1}{\sin t}$ , $\displaystyle \displaystyle \frac{1}{t}$, $\displaystyle \displaystyle \frac{1}{t^{2}}$ etc... are not locally integrable on $\displaystyle [0,\infty)$ ...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$
Use the integral expression of the Euler Mascheroni constant:
$\displaystyle \gamma=-\displaystyle\int_0^{+\infty}e^{-x}\log x\;dx$
you'll obtain:
$\displaystyle \mathcal{L}\{\log t\}=-\dfrac{\log s +\gamma}{s}$
Fernando Revilla
Maybe I missed your initial question:
Perhaps you mean that you don't see some Laplace transformed in the standard tables. The reason is that some of them, don't exist (it has been already commented by chisigma). In other cases, (for example, for the logarithmic funcion) we need some previous results.
Fernando Revilla