In this paper we determine numerical values to 80D of the coefficients in the Taylor series expansion
Γ
m
(
s
+
x
)
=
Σ
0
∞
g
k
(
m
,
s
)
x
k
{\Gamma ^m}(s + x) = \Sigma _0^\infty {g_k}(m,s){x^k}
for certain values of m and s and use these values to calculate
Γ
(
p
/
q
)
(
p
,
q
=
1
,
2
,
…
,
10
;
p
>
q
)
\Gamma (p/q)\;(p,q = 1,2, \ldots ,10;\;p > q)
and
min
x
>
0
Γ
(
x
)
{\min _{x > 0}}\Gamma (x)
to 80D. Finally, we obtain a high-precision value of the integral
∫
0
∞
(
Γ
(
x
)
)
−
1
d
x
\smallint _0^\infty {(\Gamma (x))^{ - 1}}\;dx
.