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 absolute value of the inner product between...

+ 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...

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

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...

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...

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...

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

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...

test Cauchy's convergence test Cauchy–Hadamard theorem Cauchy product Cauchy's radical test Cauchy ratio test Cauchy sequence Uniformly Cauchy sequence...

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...

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

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

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...

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...

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

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...

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...

of the ordinary product of the two polynomials are the convolution of the original two sequences. This is known as the Cauchy product of the coefficients...

\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...

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...

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

are defined and are non-zero. Some probability distributions, such as the Cauchy distribution, have undefined variance and hence ρ is not defined if X or...

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

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

− 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}}...

to Grandi's series, which is reasonable as it can be viewed as the Cauchy product of two copies of Grandi's series. 1 − 1 + 2 − 6 + 24 − 120 + ⋯ 1 + 1...

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...

In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result...