@raj2018 

Integrating formally f1^4 is a dead end for the same reason that integrating f2 is.
f1^4 contains terms of the form:

(1-x/a)^(-kc+1/2)*(1-x/b)^(-kh+1/2)

So the only possibility is to use a numerical integration.

Several errors:

1. No termination of the loop (end do is missing).
2. What do you expectto do writting f[i] = f[i+1] ?
3. n being undefined there is no chance that an hypothetical result matches the expected one (which doesn't contain n).
   Are those n typos?
    

Point 1 put apart, your problem has nothing to do with Maple: this is more a question about how you are capable or not to write correctly your recurrence relations.
Fix all these points and come again with something more consistent if you still get errors.

@Anthrazit 
Good luck

@Anthrazit 

I see...
I can't do more for you and I hope someone else will fix your problem.
As a last resort, even if I know this is a lot of work, could it be an option for you to use only Maplets?

@dharr 

For information:
Concerning the square root of symmetric positive definite matrices I submitted a question here
https://www.mapleprimes.com/questions/235834-MatrixPower-Doesnt--Give-The-Right-Answer

Extremely useful!
I agree with @C_R, a post would seem to me more appropriate and would give it more exposure.

@Preben Alsholm 

Given the definition of the integration over an infinite domain (simply definition in the sequel):

int(C, x=0..+infinity) = limit(int(C, x=0..a), a=+infinity);

one gets

limit(int(C, x=0..a), a=+infinity);
eval(%, C=0)
                       signum(C) infinity
                           undefined

In the other way

limit(int(0, x=0..a), a=+infinity);
                               0

Does this difference comes from the way eval acts?
---------------------------------------------------------------------------------------------------
Now consider this

int(0, y=0..1, x=0..+infinity);
                           undefined

But, applying the definition:

int(limit(int(0, x=0..a), a=+infinity), y=0..1);
limit(int(int(0, y=0..1), x=0..a), a=+infinity);
limit(int(0, y=0..1, x=0..a), a=+infinity);
                               0
                               0
                               0

So, do we have to consider that Maple doesn't apply the definition when it directly computes the integral?

@shreen 

Approximate_Solution.mw

@vv @Mahardika Mathematics

Even if the result is very pretty, it xwould have be nice to knowm how this (extremely complex) eqyation has beeen derived.

To @vv : give a look to this site
https://www.researchgate.net/publication/368438992_CREATING_3D_GRAPH_EQUATION_by_DHIMAS_MAHARDIKA
it contains a few other amazing images but the full article is not free.

To @Mahardika Mathematics : do you have a free paper about your work?

@Thiago_Rangel7 

If you prefer the way MMA simplifies expressions, why don't you use MMA instead of Maple?

I wonder if I'm not going to some Mapleprimes-like forum about MMA and ask
"Why doesn't MMA simplify it to (e + r)/cot(alpha/2)?", just to have an idea of what the answers will be.

The only"properties one can define for a NewDistribution those ones  List_of_properties.mw

It took me a lot of time to find where this information, and as some others about random variables, where hidden in the Statistics package.
I guess that the properties Parameters and ParentName, that any KnownDistribution has, are used elsewhere for some internal purpose.

@MaPal93 

Sorry for this late reply but I won't have much time to spend with you from now on as I have just returned to work.

Concerning your not that naive question: "by hand" simplification often involve non explicit knowledge (for instance a variance is a strictly positive quantity, a correlation coefficient rho verifies abs(rho) <= 1, and so on).
If you want Maple to simplfy an expression must set explicitely all the assumtions which seems implicit to you.

Here is your file with simplified expression for the lambdas.
(NOTE that I didn't run your code for I don't have time: I just copy-paste some expresssions into a variable Z ans simplified Z).

Analytical_SOL.mw

@RezaZanjirani 


 

Download solving.mw

@Scot Gould 

Thank you Scot

@ecterrab 

My apologies for being so late thanking you for your reply.
It lifts the veil on this mysterious (for me at least) package.

Great thanks