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I need to evaluate some (one-variable) integrals that neither SAGE nor Mathematica can do symbolically. As far as I can tell, I have two options: (a) Use GSL (via SAGE), Maxima or Mathematica to do n …

This is an update to my question Rigorous numerical integration from three years ago. Is there now a package for rigorous numerical integration that uses interval arithmetic and has access to a well- …

Let $f:\mathbb{R}_0^+\to \mathbb{R}$ be defined by some combination of the four basic operations and square roots. (The argument of square-roots is assumed is to be non-negative, and the value of squa …

I need estimates for the parabolic cylinder functions $U(a,z)$ (first studied by Whittaker). Most work in the literature focuses on $a$ real. As it happens, I am interested in $U(a,z)$ on a strip in …

I have to compute a double infinite sum to within a given accuracy $\epsilon$. Let us say the sum is of the form $$\sum_{m\geq 1} \sum_{n\geq 1} \frac{a_{m,n}}{m^2 n^2 \max(m,n)},$$ where $|a_{m,n}|\l …