No. Solr uses something similar to cosine similarity, but not exactly the same - there are some key differences.
If you go to the same link ( https://lucene.apache.org/core/4_10_0/core/org/apache/lucene/search/similarities/TFIDFSimilarity.html ) and scroll down, you will see "Lutsenko Formula Conceptual scoring "and" Lutsen "Practical scoring formula", which give more detailed information.
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