the Cauchy product is the discrete convolution of two infinite series. It is named after the French mathematician Augustin-Louis Cauchy. The Cauchy product...

The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the inner product between two vectors in an inner...

+ 3 − 4 + ... is the Cauchy product (discrete convolution) of 1 − 1 + 1 − 1 + ... with 1 − 1 + 1 − 1 + .... The Cauchy product of two infinite series...

the Cauchy–Binet formula, named after Augustin-Louis Cauchy and Jacques Philippe Marie Binet, is an identity for the determinant of the product of two...

momentum equation Cauchy–Peano theorem Cauchy principal value Cauchy problem Cauchy product Cauchy's radical test Cauchy–Rassias stability Cauchy–Riemann equations...

In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given...

In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a...

the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two...

adding series terms together term by term and the multiplication is the Cauchy product. A series or, redundantly, an infinite series, is an infinite sum. It...

turns a product of generating functions into a generating function enumerating a convolved sum of the original sequence terms (see Cauchy product). Consider...

theorem Cauchy point Cauchy principal value Cauchy problem Abstract Cauchy problem Cauchy process Cauchy product Cauchy's radical test Cauchy–Rassias...

This Cauchy product expression is justified via stars and bars: the coefficient of x n {\displaystyle x^{n}} in the expansion of the product ( 1 + x...

of Integer Sequences Recurrence relation Sequence space Operations Cauchy product Examples Discrete-time signal Farey sequence Fibonacci sequence Look-and-say...

series, again just by treating them as polynomials (see in particular Cauchy product): A B = 2 X − 6 X 2 + 14 X 3 − 26 X 4 + 44 X 5 + ⋯ . {\displaystyle...

Cauchy's inequality may refer to: the Cauchy–Schwarz inequality in a real or complex inner product space Cauchy's estimate, also called Cauchy's inequality...

mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively...

operations such as term-wise addition, term-wise multiplication, and Cauchy product. The Skolem–Mahler–Lech theorem states that the zeros of a constant-recursive...

\sum _{i=1}^{\infty }a_{\sigma (i)}=A.} Q.E.D. The Cauchy product of two series converges to the product of the sums if at least one of the series converges...

In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number...

conjg(sub(x)')*sub(y) Cauchy–Schwarz inequality Cross product Dot product representation of a graph Euclidean norm, the square-root of the self dot product Matrix multiplication...

developed several products, including a cross product represented then by [uv]. (See also: exterior algebra.) In 1853, Augustin-Louis Cauchy, a contemporary...

cn = an + bn for every n in N. The multiplication is defined as the Cauchy product, so that if c = a ⋅ b, then for each n in N, cn is the sum of all aibj...

In mathematics, an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation, is a linear homogeneous ordinary differential equation...

continuum mechanics, the Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress...

In mathematics, the tensor product V ⊗ W {\displaystyle V\otimes W} of two vector spaces V and W (over the same field) is a vector space to which is associated...

statement equivalent to the Cauchy–Binet formula. With respect to the inner product, exterior multiplication and the interior product are mutually adjoint....

In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms...

− i {\textstyle m_{n}=\sum _{i=0}^{n}a_{i}b_{n-i}} is known as the Cauchy product of the sequences a n {\displaystyle a_{n}} and b n {\displaystyle b_{n}}...

necessary that each term be its own power series. This is where the Cauchy product ( ∑ i = 0 ∞ a i x i ) ( ∑ i = 0 ∞ b i x i ) = ∑ i = 0 ∞ x i ∑ j = 0...

The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any...