Software programming requires both API reference (know-what) knowledge and programming task (know-how) knowledge. Lots of programming know-what and know-how knowledge is documented in text, for example, API reference documentation and programming tutorials. To improve knowledge accessibility and usage, several recent studies use Natural Language Processing (NLP) methods to construct API know-what knowledge graph (API-KG) and programming task know-how knowledge graph (Task-KG) from software documentation. Although being promising, current API-KG and Task-KG are independent of each other, and thus are void of inherent connections between the two types of knowledge. Our empirical study on Stack Overflow questions confirms that only 36% of the API usage problems can be answered by the know-how or the know-what knowledge alone, while the rest questions require a fusion of both. Inspired by this observation, we make the first attempt to fuse API-KG and Task-KG by API entity linking. This fusion creates nine categories of API semantic relations and two types of task semantic relations which are not present in the stand-alone API-KG or Task-KG. According to the definitions of these new API and task semantic relations, our approach dives deeper than the surface-level API linking of API-KG and Task-KG, and infers nine categories of API semantic relations from task descriptions and two types of task semantic relations with the assistance of API-KG, which enrich the declaration or syntactic relations in the current API-KG and Task-KG. Our fused and semantically-enriched API-Task KG supports coherent API/Task-centric knowledge search by text or code queries.