Let f f be an entire function with non-negative Maclaurin coefficients and let b ( r ) = r ( r f ′ ( r ) / f ( r ) ) ′ b\left ( r \right ) = r{\left ( {rf’\left ( r \right )/f\left ( r \right )} \right )’ } . It is shown that if all the zeros of f f lie in the angle | arg ⁡ z | ≤ δ \left | {\arg z} \right | \leq \delta , where 0 > δ ≤ π 0 > \delta \leq \pi , then lim sup r → ∞ b ( r ) ≥ 1 4 cose c 2 1 2 δ \lim {\sup _{r \to \infty }}b\left ( r \right ) \geq \frac {1}{4}{\text {cose}}{{\text {c}}^2}\frac {1}{2}\delta . In particular, we always have lim sup r → ∞ b ( r ) > 1 4 \lim {\sup _{r \to \infty }}b\left ( r \right ) > \frac {1}{4} for such functions.