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2. Function composition - Wikipedia

   en.wikipedia.org/wiki/Function_composition

   t. e. In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f : X → Y and g : Y → Z are composed to yield a function that maps x ...

3. Multiplicative function - Wikipedia

   en.wikipedia.org/wiki/Multiplicative_function

   Multiplicative function. In number theory, a multiplicative function is an arithmetic function f ( n) of a positive integer n with the property that f (1) = 1 and whenever a and b are coprime . An arithmetic function f ( n) is said to be completely multiplicative (or totally multiplicative) if f (1) = 1 and f ( ab) = f ( a) f ( b) holds for all ...

4. Product rule - Wikipedia

   en.wikipedia.org/wiki/Product_rule

   Miscellanea. v. t. e. In calculus, the product rule (or Leibniz rule [1] or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated in Lagrange's notation as or in Leibniz's notation as. The rule may be extended or generalized to products of three or more ...

5. Chain rule - Wikipedia

   en.wikipedia.org/wiki/Chain_rule

   t. e. In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if is the function such that for every x, then the chain rule is, in Lagrange's notation , or, equivalently, The chain rule may also be expressed in ...

6. Dirichlet convolution - Wikipedia

   en.wikipedia.org/wiki/Dirichlet_convolution

   Dirichlet convolution is a special case of the convolution multiplication for the incidence algebra of a poset, in this case the poset of positive integers ordered by divisibility. The Dirichlet hyperbola method computes the summation of a convolution in terms of its functions and their summation functions.

7. Product (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Product_(mathematics)

   Product (mathematics) In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors. For example, 21 is the product of 3 and 7 (the result of multiplication), and is the product of and (indicating that the two factors should be multiplied together).

8. Function (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Function_(mathematics)

   A function is often denoted by a letter such as f, g or h. The value of a function f at an element x of its domain (that is the element of the codomain that is associated to x) is denoted by f(x); for example, the value of f at x = 4 is denoted by f(4).

9. Convolution - Wikipedia

   en.wikipedia.org/wiki/Convolution

   The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The integral is evaluated for all values of shift, producing the convolution function.