All Questions

I'm looking for references which derive the Lagrange inversion formula, given below (in bold), for the Taylor series coefficients of the compositional inverse of a function $f$ analytic at the origin ...

Consider the following integral equation: $$\int_0^\infty K(t,y)\phi(t,x)dt=0$$ Here, $K(t,y)$ is a trigonometric kernel and $\phi(t,x)$ is monotonic wrt $x$ ( for fixed $t$). I want to find the ...

There exist a "standard" or canonical way to construct a real valued function whose Mellin transform has a prescribed set of zeroes? Clearly for some set of zeroes this could be impossible ...