First-day sales of “The Simpsons: Season 3” DVD doubled those of the Season 1 DVD release and were about 20% ahead of the Season 2 box, according to Fox executives. Released Tuesday, it is estimated to have already sold through about 40% of its initial shipment of about 500,000 DVD units. A half-million units is a fraction of what major theatrical titles ship to retail outlets and video rental stores, but for the TV-to-DVD niche, it is a large shipment. The industry has found that seasonal DVD releases of series’ such as HBO’s “The Sopranos” can be rather lucrative because each box set retails for about $50, compared with about $20 for a major theatrical release. The increased profit margins and the length of time TV-to-DVD product tends to remain selling on store shelves has made TV-to-DVD products one of the hottest growth sectors in the realm of DVD, several industry sources said.