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In discrete calculus the indefinite sum operator (also known as the antidifference operator), denoted by or , [1] [2] is the linear operator, inverse of the forward difference operator. It relates to the forward difference operator as the indefinite integral relates to the derivative .
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
The cast operator is not overloadable, but one can write a conversion operator method which lives in the target class. Conversion methods can define two varieties of operators, implicit and explicit conversion operators. The implicit operator will cast without specifying with the cast operator (()) and the explicit operator requires it to be used.
In mathematics, an operator or transform is a function from one space of functions to another. Operators occur commonly in engineering, physics and mathematics. Many are integral operators and differential operators. In the following L is an operator :
2 Connection to indefinite sum. 3 Alternative usage. 4 Rules. 5 List of indefinite products. ... the indefinite product operator is the inverse operator of (()) = ...
Empty sum, a sum with no terms; Indefinite sum, the inverse of a finite difference; Kronecker sum, an operation considered a kind of addition for matrices; Matrix addition, in linear algebra; Minkowski addition, a sum of two subsets of a vector space; Power sum symmetric polynomial, in commutative algebra; Prefix sum, in computing
[1] [2] [a] Such operators often preserve properties, such as continuity. For example, differentiation and indefinite integration are linear operators; operators that are built from them are called differential operators, integral operators or integro-differential operators. Operator is also used for denoting the symbol of a mathematical operation.
Most of the operators available in C and C++ are also available in other C-family languages such as C#, D, Java, Perl, and PHP with the same precedence, associativity, and semantics. Many operators specified by a sequence of symbols are commonly referred to by a name that consists of the name of each symbol.