抄録
Let
G be the multiplicative group generated by the gamma functions Γ(
ax + 1) (
a = 1
, 2
,...), and
H be the subgroup of all elements of
G that converge to non-zero constants as
x →∞. The quotient group
G/H is the group of equivalence classes of
G, where
ƒand
g are equivalent ⇔
ƒ∼
Cg (
x →∞) for some
C ≠ 0. We show that
G/H ~ Q
+. Similar consideration is possible for the case that the gamma functions Γ(
ax + 1) with
a ∈R
+ are concerned, and we show that
G/H ~ Z × R × R. Also, several concrete examples of the elements of
H are constructed, e.g. it holds that
/ 
→
(
n →∞), where
denotes a multinomial coefficient.
