European Call Option With Infinite Maturity

What is the value of a vanilla European call option as the time to maturity $T \to \infty$? Assume the Black-Scholes framework with constant volatility $\sigma$, constant risk-free rate $r > 0$, spot price $S$, and strike $K$. Consider two cases: 1. The underlying pays **no dividends** ($q = 0$). 2. The underlying pays a **continuous dividend yield** $q > 0$.