I am trying the evaluate the following limit $$\lim_{r\to 1^-}\frac{\xi'\left(\frac{1}{1-r}\right)}{(1-r)\ \xi\left(\frac{1}{1-r}\right)} $$ where $\xi$ denotes the Riemann xi function.
Let $$L=\lim_{r\to 1^-}\frac{\xi'\left(\frac{1}{1-r}\right)}{(1-r)\ \xi\left(\frac{1}{1-r}\right)} $$ Since the above limit is of the form $\frac{\infty}{\infty}$ so using L'Hôpital's rule we get $$L=\lim_{r\to 1^-}\frac{\xi''\left(\frac{1}{1-r}\right).\frac{1}{(1-r)^2}}{\frac{1}{(1-r)}.\xi'\left(\frac{1}{1-r}\right)-\xi\left(\frac{1}{1-r}\right)} $$ So on simplification we get $$L=\lim_{r\to 1^-}\frac{\xi''\left(\frac{1}{1-r}\right).\frac{1}{(1-r)}}{\xi'\left(\frac{1}{1-r}\right)-(1-r)\ \xi\left(\frac{1}{1-r}\right)} $$ Can we evaluate this limit using sage math? I am struggling to find this limit. Any help will be appreciated.