Res[ ((s^3)*(exp(1/s))) ] in Matlab

Sir,

i want to evaluate the Residue of the function

   F(s)= ((s^3)*(exp(1/s)))

in Matlab, so how can i do it?

with thanks

[Star Strider]

No partial fraction expansion exists for your expression.

[Sourav Kumar]

Hi Star , so can't we find its Residue in Matlab??

[Star Strider]

That would be my assessment.

To do a partial fraction expansion, you have to have a series of symbolic fractions in ‘s’.

Answer 1

[David Goodmanson]

Hi Sourav,

The function has an essential singularity at s = 0, but you can still expand exp(1/s) in a Taylor series in 1/s, just as if it were a Taylor series for exp(x), i.e.

exp(1/s) = 1 + c_1*(1/s) + c_2*(1/s)^2 + c_3*(1/s)^3 + ...

where the Taylor coefficients c_1 etc. you should know. Then multiply everything by s^3, and the find the coefficient of the term that now goes like 1/s. The residue is positive and < .05

[Sourav Kumar]

Hi David , how you have came to the result that "The residue is positive and < .05"??,it will be very kind of you if you explain the same

[John D'Errico]

Sourav - since this is clearly a homework problem, I assume that David does not wish to do all of the work for you. He told you exactly what to do however. He knows the result, because he did the computation that he told you to do. It is quite easy to do. So why not make an effort? The reason he told you it is positive and less than 0.05, is so that you can know if you got it correct.

[David Goodmanson]

Hi Sourav,

What John said is true in all respects. The Taylor series for an exponential is probably the most common example there is, and I think you can get this with a bit of effort. Due to other things going on I won't be getting back to site for awhile, but if it doesn't work out and you show what you have done, John or others on this site can help.