In Sewall Wright's Evolution of Mendalian Population, the equation for the nonrecurrent mutation is $$\frac{\phi(x)}n = \binom n {nx}\int_0^1 q^{nx}(1-q)^{n(1-x)}\phi(q)\,dq,\quad \forall x\in[0,1],$$ where $n>0$ and $\binom a b$ is the binomial coefficient. We are to solve for a nonzero function $\phi\ne0$. It is an eigenvalue problem of a compact operator (Fredholm equation of the second kind). But what is a general method for solving this integral equation? dirichlet Is there a transform, say Mellin transform, that does the trick?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.