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I want to approximate an integral of the form $$\int_a^bf(t)e^{ig(t)}dt,$$where $f(t)$ is smooth, $g(t)$ is real-valued and smooth. The stationary phase method says that if $t_0\in [a,b]$ is such that ...

To celebrate the new year and the future of mathematics (or the mathematics of future), I see no better way to ask a question stemming from my researches on power series. The two papers the title ...

I'm interested in Singularity Analysis after reading this Math.Stack post. In the "Analytic Combinatorics" book by P. Flajolet and R. Sedgewick, at p.390, the following transfer theorem (...

As increasingly higher degree terms are added to a "random" polynomial, the roots of a polynomial can be proven to approach the unit circle. For example, see the MathOverflow question Why ...

Is the following theorem known, or can be easily derived from known results? Consider the differential equation $$w''-kz^{-1}w'=(\lambda+\phi(z))w,$$ where $k>0$ is fixed, $\lambda$ is a large (...