Continued Fractions and Irrationality Measures for Chowla--Selberg Gamma Quotients

We give 39 rapidly convergent continued fractions for Chowla–Selberg gamma quotients, and deduce good irrationality measures for 20 of them, including for $\mathrm{CS}(-3)=(\mathrm{\Gamma }(1\mathrm{/}3)\mathrm{/}\mathrm{\Gamma }(2\mathrm{/}3){)}^3$, for $a^{1\mathrm{/}4}\mathrm{CS}(-4)=a^{1\mathrm{/}4}(\mathrm{\Gamma }(1\mathrm{/}4)\mathrm{/}\mathrm{\Gamma }(3\mathrm{/}4){)}^2$ with $a=12$ and $a=1\mathrm{/}5$, and for $\mathrm{CS}(-7)=\mathrm{\Gamma }(1\mathrm{/}7)\mathrm{\Gamma }(2\mathrm{/}7)\mathrm{\Gamma }(4\mathrm{/}7)\mathrm{/}(\mathrm{\Gamma }(3\mathrm{/}7)\mathrm{\Gamma }(5\mathrm{/}7)\mathrm{\Gamma }(6\mathrm{/}7))$. These appear to be the first proved and reasonable irrationality measures for gamma quotients.