SQLサーバーの組み込み関数のリストを取得する方法はありますか？

これを試してください

SELECT name, definition, type_desc 
FROM sys.sql_modules m 
INNER JOIN sys.objects o ON m.object_id=o.object_id
WHERE type_desc like '%function%'

または：

SELECT * FROM sys.all_objects where type in ('FN','AF','FS','FT','IF','TF')

タイプは次のとおりです。

--AF = Aggregate function (CLR)
--C = CHECK constraint
--D = DEFAULT (constraint or stand-alone)
--F = FOREIGN KEY constraint
--PK = PRIMARY KEY constraint
--P = SQL stored procedure
--PC = Assembly (CLR) stored procedure
--FN = SQL scalar-function
--FS = Assembly (CLR) scalar function
--FT = Assembly (CLR) table-valued function
--R = Rule (old-style, stand-alone)
--RF = Replication filter procedure
--SN = Synonym
--SQ = Service queue
--TA = Assembly (CLR) trigger
--TR = SQL trigger 
--IF = SQL inlined table-valued function
--TF = SQL table-valued function
--U = Table (user-defined)
--UQ = UNIQUE constraint
--V = View
--X = Extended stored procedure
--IT = Internal table

組み込み関数