Reciprocal gamma function

In mathematics, the reciprocal gamma function is the function where Γ(z) denotes the gamma function. Since the gamma function is meromorphic and nonzero everywhere in the complex plane, its reciprocal is an entire function. As an entire function, it is of order 1 (meaning that log log |1/Γ(z)| grows no faster than log |z|), but of infinite type (meaning that log |1/Γ(z)| grows faster than any multiple of |z|, since its growth is approximately proportional to |z| log |z| in the left-hand plane).

Reciprocal gamma function

In mathematics, the reciprocal gamma function is the function where Γ(z) denotes the gamma function. Since the gamma function is meromorphic and nonzero everywhere in the complex plane, its reciprocal is an entire function. As an entire function, it is of order 1 (meaning that log log |1/Γ(z)| grows no faster than log |z|), but of infinite type (meaning that log |1/Γ(z)| grows faster than any multiple of |z|, since its growth is approximately proportional to |z| log |z| in the left-hand plane).