@Ramakrishnan 

Thank you for the code.

Can we deduce the value of x[30] using your method.

@tomleslie 

Thank you for your code.

I used a theoretical method and by hand I get the same result.

But your code is very nice.

How can we deduce the value of x[30]

many thanks

@Carl Love 

thank you. It's working. I get the same values.

@Carl Love 

Thank you for this nice code.

I get this message.

ChiSqIndTest(DrugTrial, method = G);
Error, (in ChiSqIndTest) invalid input: add expects 2 arguments, but received 1

@Carl Love 

Thank you for remark,

I think the denominator in your definition is T[i,j] and not T[i,j]^2 .

@Carl Love 

Thank your for general method.

Is there any method to get the asymptotic behavior of the solution in general case using bessel function

@Carl Love 

I agree with you. Its a good remark, so we must use a numerical method.

@vv 

I really, appreciate your help. Thank you

@vv 

great.

Let for example n=5;

lambda=1/4;

mu=1/2;

P[0](t)=exp(-t);

t in (0,+infinity)

Thanks

@vv 

Thanks for your idea.

Is there any way to plot P[n](t) for a range of t for example t in (0,100).

one again, thank you for your idea

@tomleslie 

Many thanks I agree with you

@tomleslie 

I agree with you, there is something not clear which option 1 or 2 is correct and why when we change the boundary condition one get the solution 

@rlopez 

The system of equation is correct. It comes from Finite difference method and we add some boundary condition.

I we change sin(Pi*i*h) by zero we get the solution.

Please see modified code

eqProb.mw

With zero as boundary condition i obtain a solution 

what do you think

@tomleslie 

Thnak you for your idea, as fsolve can not give the solution, maybe one can use iterative method to get an approximate solution

@Preben Alsholm 

Its a good answer, I verified directly i find the same solution.

Using maple can we simplify diff(g(x),x) to get an answer using piecewise function maybe we can use convert diff(g(x),x) using piecewise function

Many thanks