How to solve this recursive integral? I do not even begin to understand how to solve this recursive integral. This doesn't even seem possible?
$$H{(x, y)} = \int_{t=0}^{t=2\pi} H(\frac{xt}{2},\frac{xt}{2})*2xt dt$$
This is intriguing me. What approaches exist for solving this?
EDIT:$$H{(x)} = \int_{t=0}^{t=2\pi} H\big(\frac{xt}{2}\big)*2xt \, dt$$
A partial answer for the second integral
Consider the function $G(x) = xH(x/8)$. Rescaling $x$ in the integral and making the appropriate $u$-substitution gives $$ G(x) = \int_0^{\pi x} G(u) du $$ Differentiating both sides gives $$ G'(x) = G(\pi x) $$ a rather curious differential equation I'm not sure of the solution to.