"A Transact- SQL function defined by a user. Functions encapsulate frequently performed logic in a named entity that can be called by Transact-SQL statements instead of recoding the logic in each statement." (Microsoft Corporation, Microsoft SQL Server 2000 system administration, 2001)
"Functions that you write as opposed to built-in functions supplied by a programming language." (Greg Perry, "Sams Teach Yourself Beginning Programming in 24 Hours" 2nd Ed., 2001)
"A user-defined function is a Transact-SQL function defined by a user. Functions encapsulate frequently performed logic in a named entity that can be called by Transact-SQL statements instead of recoding the logic in each statement." (Anthony Sequeira & Brian Alderman, "The SQL Server 2000 Book", 2003)
"A function that is written by an analyst, user, or database administrator and does not come as part of the default installation of the Oracle server software." (Bob Bryla, "Oracle Database Foundations", 2004)
"A collection of T-SQL statements with a well-defined set of input parameters, but only one output which can be a scalar value or a table. User-defined functions allow the encapsulation of various logical and database operations, but cannot be used to affect changes to a database." (Thomas Moore, "EXAM CRAM™ 2: Designing and Implementing Databases with SQL Server 2000 Enterprise Edition", 2005)
"A Transact-SQL function defined by a user. Functions encapsulate frequently performed logic in a named entity that can be called by Transact-SQL statements instead of recoding the logic in each statement." (Microsoft Docs, SQL Server 2005)
"Extensible code added to the DBMS to be callable like built-in database functions." (Craig S Mullins, "Database Administration" 2nd Ed, 2012)
"A function that is defined to the DB2 database system by using the CREATE FUNCTION statement and that can be referenced thereafter in SQL statements." (Sybase, "Open Server Server-Library/C Reference Manual", 2019)
"In SQL Server, a Transact-SQL function defined by a user." (Microsoft Technet)
"A user-defined routine that returns at least one value. (IBM)
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