# Tagged Questions

Questions on special functions, useful functions that frequently appear in pure and applied mathematics (usually not including "elementary" functions).

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### A conjectured asymptotic expansion of a function related to the sine and cosine integrals

Recall the definitions of the sine and cosine integrals:$$\operatorname{Si}(x)=\int_0^x\frac{\sin t}t dt,\quad\operatorname{si}(x)=-\int_x^\infty\frac{\sin t}t dt=\operatorname{Si}(x)-\frac\pi2,\tag1$$...
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### The Monster PolyLog Integral $\int_0^\infty \frac{Li_n(-\sigma x)Li_m(-\omega x^2)}{x^3}dx$

I am trying to solve this integral $$\int_{0}^{\infty} {{\rm Li}_{n}\left(-\sigma x\right){\rm Li}_m\left(-\omega x^{2}\right) \over x^{3}}\,{\rm d}x$$ which is from some high school training ...
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### Separate incomplete elliptic integral into real and imaginary parts

I am working in a problem that involves Incomplete Elliptic Integrals of the First and Second kind of the form $F(\sin^{-1}x~|~m)$ and $E(\sin^{-1}x~|~m)$ where the parameters $m$, $x$ are real ...
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### Possible error in Wood's report on polylogarithms

I'm studying the article by Wood, D.C. "The Computation of Polylogarithms. Technical Report 15-92*" PS (it is remarkably poorly translated from latex to ps). It is listed in the literature section on ...
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### The Tribonacci constant and the Dragon

Let $x = \frac{\ln T}{\ln 2} = 0.879146\dots$ where $T$ is the tribonacci constant, then x solves the transcendental equation, $$4^x(2^x-1)=(2^x+1)$$ Let $x = \frac{\ln y}{\ln 2} = 1.523627\dots$ ...