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Watson worked on a wide variety of topics, all within the area of complex variable theory, such as difference equations, differential equations, number theory and special functions. He is best known as a joint author with Whittaker of A Course of Modern Analysis published in 1915. The first edition of the book has only Whittaker as an author.
Watson undertook a major work on Ramanujan's notebooks, extending his results and supplying proofs. He enjoyed numerical calculations and spent many happy hours doing numerical work on his calculating machine. He was elected to the Royal Society in 1919.
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