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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 ...
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 ...
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.
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 ...
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 ...
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product is a product distribution .
Multiplication theorem. In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values; thus the name. The various relations all stem from the same underlying principle; that is, the relation ...
The Cartesian product of two edges is a cycle on four vertices: K 2 K 2 = C 4. The Cartesian product of K 2 and a path graph is a ladder graph. The Cartesian product of two path graphs is a grid graph. ( K 2 ) n = Q n . {\displaystyle (K_ {2})^ {\square n}=Q_ {n}.} Thus, the Cartesian product of two hypercube graphs is another hypercube: Q i Q ...
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