In this paper, we determine the radius of
λ
-uniform convexity,
λ
-starlikeness, and
α
-convexity of order
δ
for the Weierstrass canonical product of an entire function as a root having smallest modulus and argument
ϕ
of a functional equation. As special cases, we also determine the radius of
λ
-uniform convexity,
λ
-starlikeness, and
α
-convexity of order
δ
for the entire function
1
/
Γ
.