Can anyone identify these constants?

[Eric W. Weisstein]

Can anyone get these in closed form (assuming they exist, which seems to 
be the case):

Limit[Log[10, Hypergeometric2F1[(1/2)*(1 - n), (-(1/2))*n, 2, 4]]/n, n -> Infinity]
http://www.research.att.com/projects/OEIS?Anum=A114473
0.47712...

Limit[Log[10, Hypergeometric2F1[-n + 1, n + 2, 2, -1]]/n, n -> Infinity]
Limit[Log[10, Hypergeometric2F1[-n + 1, n + 1, 1, -1]]/n, n -> Infinity]
http://www.research.att.com/projects/OEIS?Anum=A114470
http://www.research.att.com/projects/OEIS?Anum=A114472
0.76555...

http://www.research.att.com/projects/OEIS?Anum=A114467
http://www.research.att.com/projects/OEIS?Anum=A114468
0.434286...

?

Cheers,
-Eric