Recent content by mahmud_dbm

Dear Friends So, i have this special case where i have to do a differentiation and summation. Please check the following. Is it okay ?? Or, i how should i proceed with this ?

please let me know if it's okay! that's how far i have gone, probably it's wrong.

Thank you so much for your reply, You are right, here x is a vector and H is a matrix, and i want to differentiate Hx with respect to x Here's the complete problem that's how far i have gone, probably it's wrong.

I need some help with an Integration. Here's the equation I = ##\int_0^∞ \frac {x^{n+1}} {1 + x^n} ⋅ e^{-x^2/{2 \sigma^2}} ## I have tried to solve the equation by simplifying first like let, ## \frac x {\sqrt 2 \sigma} = v ##, so the ##x = v \sqrt 2 \sigma## then, ##dx = \sqrt 2 \sigma d...

Okay so, now you can omit that optional constant part, which i haven't included, and it's a^2, not a, it was a mistake in the first post. But, like i said, a=1, so it wouldn't make any difference, in my case.

Right Right, x's be t's, there is no x in the equation.

Dear Ray Another constant can be multiplied sometimes which is (2/a^4), this is optional. There is a little change from the 1st post, it's a^2 instead of a. It's a constant, so doesn't make any difference. Other values are like alpha = 0.1, a=1, m=3 (usually >1), A = 0.02. You are right...

Ray Surely your reply helped me a lot, now i understand the problem at least. Thank you so much for your time. Using MATLAB, i would probably get the numerical value but i won't be able to explain how i got that. That's why i needed the explanation. I will share if i can find anything. Thank...

MATLAB gave me a numerical answer i need to know the how and the formula.

Ray I simply wrote the function, integrated using built-in integration function. bt=0.02; s=1; g=3; a=0.1; k=g*s/bt; p=1/g; b=a*bt^p; C=2*s*bt^p; fun=@(y) (C/k^3)*((y-1).^2.*exp(-(y-1)./k).^2.*y.^p)./(1+b.*y.^p); m=integral(fun,0,Inf); the m is now 0.6839.

Dear Chet The answer should be just a value, for the given parameters, so it should be in closed form, but now i doubt if it's possible. So, finite or infinite solution, please do enlighten me.

Ray I mean, as i said earlier m>1, so that means p is fractional. How do i expand that fractional power thing?

Dear Sir Thank you so much for you reply and thorough analysis. Sir, in the 4th line, should it be exp(-v^2) ? And sir, i tried with MATLAB, it's showing values. I don't know how they got the value. and what did you mean by "expand things in convergent infinite series", how do i expand that...

Dear Ray Thank you so much. I already see some lights. Now as you said, if the parameter values were given, then it could be solved. Now, you were right in assuming a>0, because a = 0.1, m = 1, 2, 3, 4, 5 upto 20. So, yes k>0. But I want to understand how did you come up with all the right...