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 (...

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

^{2}J_{\nu }^{2}(x)={\frac {x^{2}}{2}}.} 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 +...

{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...

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

{\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...

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

theorem can be proven using concepts from the theory of groups: The residue classes modulo n that are coprime to n form a group under multiplication (see...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

described using Laguerre polynomials. Erdélyi gives the following two multiplication theorems t n + 1 + α e ( 1 − t ) z L n ( α ) ( z t ) = ∑ k = n ∞ ( k n )...

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on...

2} in the multiplicative group ( Z / q Z ) ∗ {\displaystyle (\mathbb {Z} /q\mathbb {Z} )^{*}} is p {\displaystyle p} . By Lagrange's theorem, the order...

(complex analysis) Hölder's theorem (mathematical analysis) Multiplication theorem (special functions) Carathéodory's existence theorem (ordinary differential...

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 the mathematical discipline of group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup...

In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent...

Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing...

Linear speedup theorem, that the space and time requirements of a Turing machine solving a decision problem can be reduced by a multiplicative constant factor...

function rule expresses its derivative as the multiplicative inverse of the derivative of f. The theorem applies verbatim to complex-valued functions of...

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...

The Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a...

{\displaystyle p} . Two series may be multiplied (sometimes called the multiplication theorem): For any two arithmetic functions f {\displaystyle f} and g {\displaystyle...

+ 2 x n B n ( 1 2 ) = ( 1 2 n − 1 − 1 ) B n , n ≥ 0  from the multiplication theorems below. {\displaystyle {\begin{aligned}B_{n}(1-x)&=\left(-1\right)^{n}B_{n}(x)...

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

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

property of multiplication over addition and combining like terms, but it can also be done (perhaps more easily) with the multinomial theorem. It is possible...

polynomial). The theorem is a special case of the polynomial remainder theorem. The theorem results from basic properties of addition and multiplication. It follows...