  Large Language Models (LLMs) are foundational in language technologies,
particularly in information retrieval (IR). Previous studies have utilized LLMs
for query expansion, achieving notable improvements in IR. In this paper, we
thoroughly explore the best practice of leveraging LLMs for query expansion. To
this end, we introduce a training-free, straightforward yet effective framework
called Multi-Text Generation Integration (\textsc{MuGI}). It leverages LLMs to
generate multiple pseudo-references, integrating them with queries to enhance
both sparse and dense retrievers. Our empirical findings reveal that: (1)
Increasing the number of samples from LLMs benefits IR systems; (2) A balance
between the query and pseudo-documents, and an effective integration strategy,
is critical for high performance; (3) Contextual information from LLMs is
essential, even boost a 23M model to outperform a 7B baseline model; (4) Pseudo
relevance feedback can further calibrate queries for improved performance; and
(5) Query expansion is widely applicable and versatile, consistently enhancing
models ranging from 23M to 7B parameters. Our code and all generated references
are made available at \url{https://github.com/lezhang7/Retrieval_MuGI}
