Logarithm of the Cumulative Distribution Function for a Student's t distribution.

1. The formula for F(x;nu) in the documentation is only valid for x>0.

Wikipedia uses t (not x), but gives the same formula, but for t>0 only:

From "Sampling Student’s T distribution – use of the inverse cumulative distribution function" by William T. Shaw:

And the same formula is returned by `wolframscript`:

2. There is a problem in the implementation of `logcdf`.
The implementation basically computes the normal cdf-probability and then takes the logarithm.
This defeats the purpose of having a `logcdf`, which is meant to be used when `cdf(x)` is
so small it is rounded to 0.

The formula for `cdf` uses the incomplete beta function, which in turn uses `beta`.
Your project includes an `betaln` which computes the logarithm of a beta value.
A solution must be to use `betaln` to implement an "logarithm of a regularized, incomplete beta function"
and use that to implement `logcdf`.