THE B AND T FUNCTIONS 
271 
We now use 213, 5). 
Let us note that by virtue of 1, 2 the value of G is known for 
all u > 0, when it is known in the interval (0, 1). By virtue of 
5) G is known for u < 0 when its value is known for u > 0. 
Moreover the relation 5) shows the value of Gr is known in (|-, 1) 
when its value is known in (0, |). 
As a result of this we see Gr is known when its values in the 
interval (0, |) are known; or indeed in any interval of length 
Gauss has given a table of log G(u) for l<w<1.5 calculated, 
to 20 decimal places. A four-place table is given in “ A Short 
Table of Integrals ” by B. 0. Peirce, for 1 < u < 2. 
ff(i) = Vtt. 
(6 
5. 
For in 5) set u = \ 
Then 
6? 2 (1) = TT. 
Gì ( I ) = ± vAr. 
Hence 
We must take the plus sign here, since Gr > 0 when u > 0, by 221. 
6. 
O 
where n is a positive integer. 
Similarly 
Thus 
226. Expressions for log Gr(u), and its Derivatives. 
From 224, 1) we have for u > 0, 
L(u) = log G (u) = - Oil — log u + 2} — log ^1 + ^} • ( 1 
Differentiating, we get 
That this step is permissible follows from 155, l.