2
votes
2answers
54 views

Uniform convergence of matrix integral sequence

I was given recursively defined: $M_k=I+\int_{t_0}^tA(s)M_{k-1}(s)~ds$ and $M_0=I$ and that $A(t)$ is a matrix with entries that are continuous functions on $t_0\leq t\leq t_1$. By induction we can ...
2
votes
2answers
68 views

Integral expansion help!

So I'm very close to finishing a proof of the exponential function in terms of differential equations. For this next step, I have to show the following. For $n \ge 0$ define $E_n (t)$ recursively ...
4
votes
1answer
166 views

Recurrence relation for a function with an integral of the function?

Pardon my lack of tex skills, but what is the recommended procedure in the following scenario: $$g(f) = 1+\int_0^{1-f} g\left(\dfrac{f}{1-x}\right)\,dx$$ I am not sure how to proceed in such a ...
2
votes
1answer
386 views

How to solve this recurrence relation? (convolution integral)

Following is a recurrence relation written by Robert Israel from Poisson arrivals followed by locking $u_n(t) = \int_0^{t-nT} \lambda \exp(-\lambda y) u_{n-1}(t-y-T)\, dy$. The solution he ...