Multiplication theorem information

In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit...

spaces. In general, the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators, which are as simple as...

because of its recurrence equation, for all rational arguments. The multiplication theorem of the Γ {\displaystyle \Gamma } -function is equivalent to ψ (...

domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various...

{m}(x)+\left(1-x^{2}\right)P'_{m}(x)\right).\end{aligned}}} The multiplication theorem gives k m + 1 ψ ( m ) ( k z ) = ∑ n = 0 k − 1 ψ ( m ) ( z + n k...

transcendental under the same assumptions. The Bessel functions obey a multiplication theorem λ − ν J ν ( λ z ) = ∑ n = 0 ∞ 1 n ! ( ( 1 − λ 2 ) z 2 ) n J ν +...

near the multiplication theorem.[clarification needed] The next contributor of importance is Binet (1811, 1812), who formally stated the theorem relating...

{3(s-3)}{7+z-s+{\cfrac {4(s-4)}{9+z-s+\ddots }}}}}}}}}}} The following multiplication theorem holds true: Γ ( s , z ) = 1 t s ∑ i = 0 ∞ ( 1 − 1 t ) i i ! Γ (...

{\displaystyle U(a,b,z)=z^{1-b}U\left(1+a-b,2-b,z\right)} . The following multiplication theorems hold true: U ( a , b , z ) = e ( 1 − t ) z ∑ i = 0 ( t − 1 ) i...

}}\;\Gamma (2z).} The duplication formula is a special case of the multiplication theorem (see  Eq. 5.5.6): ∏ k = 0 m − 1 Γ ( z + k m ) = ( 2 π ) m − 1 2...

with the multiplication given by convolution. If one takes, for example, S = N d {\displaystyle S=\mathbb {N} ^{d}} , then the multiplication on C [ S...

In mathematics, the multiplicative ergodic theorem, or Oseledets theorem provides the theoretical background for computation of Lyapunov exponents of a...

The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a divide-and-conquer...

specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow...

invertible matrices, do not form an abelian group under multiplication because matrix multiplication is generally not commutative. However, some groups of...

equilibrium theorem (economics) Multinomial theorem (algebra, combinatorics) Multiplication theorem (special functions) Multiplicity-one theorem (group representations)...

A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient...

Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms...

group Multiplicative group of integers modulo n Other important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's...

mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer...

the action of any group on itself by left multiplication is free. This observation implies Cayley's theorem that any group can be embedded in a symmetric...

mathematics and group theory, the term multiplicative group refers to one of the following concepts: the group under multiplication of the invertible elements of...