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...

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- Dec 26th 2010, 06:20 AMvishnuk5320Laplace transform
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... - Dec 26th 2010, 07:16 AMchisigma
The question has to be proposed in a more precise form!... for example the 'logarithmic function' $\displaystyle \ln t$ is perfectly L-transformable...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Dec 26th 2010, 07:41 AMchisigma
... 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

$\displaystyle \chi$ $\displaystyle \sigma$ - Dec 27th 2010, 12:39 AMvishnuk5320
i mean L(log t).....

- Dec 27th 2010, 02:10 AMFernandoRevilla
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 - Dec 27th 2010, 10:55 AMFernandoRevilla
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