Continued Fractions and Irrationality Measures for Chowla--Selberg Gamma Quotients
Abstract
We give 39 rapidly convergent continued fractions for Chowla--Selberg gamma quotients, and deduce good irrationality measures for 20 of them, including for CS(-3)=((1/3)/(2/3))3, for a1/4CS(-4)=a1/4((1/4)/(3/4))2 with a=12 and a=1/5, and for CS(-7)=(1/7)(2/7)(4/7)/((3/7)(5/7)(6/7)). These appear to be the first proved and reasonable irrationality measures for gamma quotients.
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