Light field cameras (LFCs) have received increasing attention due to their wide-spread applications. However, current LFCs suffer from the well-known spatio-angular trade-off, which is considered an inherent and fundamental limit for LFC designs. In this paper, by doing a detailed optical analysis of the sampling process in an LFC, we show that the effective resolution is generally higher than the number of micro-lenses. This contribution makes it theoretically possible to super-resolve a light field. Further optical analysis proves the "2D predictable series" nature of the 4D light field, which provides new insights for analyzing light field using series processing techniques. To model this nature, a specifically designed epipolar plane image (EPI) based CNN-LSTM network is proposed to super-resolve a light field in the spatial and angular dimensions simultaneously. Rather than leveraging semantic information, our network focuses on extracting geometric continuity in the EPI domain. This gives our method an improved generalization ability and makes it applicable to a wide range of previously unseen scenes. Experiments on both synthetic and real light fields demonstrate the improvements over state-of-the-arts, especially in large disparity areas.