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 ?
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.
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...
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.
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...