natural log of pi to sixty digits, a reference needed I have found a table of the logs of gamma functions at basic fractions, accurate to 60 decimal digits.  It omits $\ln(\Gamma(1/2)) = \ln(\pi)/2$ and I want that number.  
Where is a cit-able source that contains this this number to high accuracy?
 A: Here it is, to 80 digits.
0.57236494292470008707171367567652935582364740645765578575681153573606\
888494241304
Youcan cite me, "personal communication".
A: I know that you are asking for a table or software where you can just look this up, but this number is quickly computable to high accuracy with the right approach. (Assuming that you have an engine that can keep track of high precision in the first place.)
To speed up computations, use that $$\ln(\pi)=\ln\left(\frac{\pi}{22/7}\right)+\ln(2)+\ln(11)-\ln(7)$$ The latter three terms can be looked up to high precision, and now you have to find $\ln(7\pi/22)$, where $7\pi/22$ is very close to $1$. In fact $|1-7\pi/22|<0.00041$. So even the slowly converging Taylor series for $\ln$ can output a result quickly, assuming that you again use a table, this time to look up many digits of $\pi$.
$$\begin{align}
\ln(1+(7\pi/22-1)) & = -\sum_{n=1}^\infty\frac{(-1)^n}{n}(7\pi/22-1)^n
\end{align}$$
Since $(7\pi/22-1)<0$, we do not really have an alternating series, and we'll have to think about Taylor's error bound. The $n+1$st derivative of $\ln(1+x)$ is $(-1)^{n}n!/(1+x)^{n+1}$. On the interval $[-0.00041,0.00041]$, this is bounded in absolute value by $n!/0.99959^{n+1}$. So an error bound for the $n$th partial sum would be $$\frac{n!/0.99959^{n+1}}{(n+1)!}0.00041^{n+1}=\frac{1}{n+1}\left(\frac{0.00041}{0.99959}\right)^{n+1}$$ Using $n=17$ brings this under $10^{-62}$. 
At present, I do not have access to an engine that could keep track of enough decimal precision, or else I would conclude my answer with the end result of this process. But here is the formula it yields, with an absolute error bound of less than $10^{-62}$:$$\ln(\pi)\approx-\sum_{n=1}^{17}\frac{(-1)^n}{n}(7\pi/22-1)^n+\ln(2)+\ln(11)-\ln(7)$$
A: (In know this question is old and answered, but...) For $\ln(\pi)$ the Online Encycolpedia of Integer Sequences has a value to 105 decimal places. It is also citable.
