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Added documentation + test of effect of n_taylor #5327

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Run time

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Job	Run time
build (macos-latest, 3.10) / build	3m 28s
build (macos-latest, 3.11) / build	2m 30s
build (macos-latest, 3.9) / build	3m 4s
build (ubuntu-latest, 3.10) / build	2m 23s
build (ubuntu-latest, 3.11) / build	2m 23s
build (ubuntu-latest, 3.9) / build	2m 41s
build (windows-latest, 3.10) / build	3m 45s
build (windows-latest, 3.11) / build	3m 53s
build (windows-latest, 3.9) / build	3m 47s
	27m 54s