Sigma function information

mathematics, by sigma function one can mean one of the following: The sum-of-divisors function σa(n), an arithmetic function Weierstrass sigma function, related...

theory, σ is included in various divisor functions, especially the sigma function or sum-of-divisors function. In applied mathematics, σ(T) denotes the...

between the sigma, zeta, and ℘ {\displaystyle \wp } functions is analogous to that between the sine, cotangent, and squared cosecant functions: the logarithmic...

{\displaystyle g(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}\exp \left(-{\frac {1}{2}}{\frac {(x-\mu )^{2}}{\sigma ^{2}}}\right).} Gaussian functions are widely used in...

the number-of-divisors function (OEIS: A000005). When z is 1, the function is called the sigma function or sum-of-divisors function, and the subscript is...

\sigma =|a|} ) The Barnes G-function ( σ {\displaystyle \sigma } is infinite). exp ⁡ ( exp ⁡ ( z ) ) {\displaystyle \exp(\exp(z))} Entire functions of...

probabilities. Formally, the standard (unit) softmax function σ : R K → ( 0 , 1 ) K {\displaystyle \sigma \colon \mathbb {R} ^{K}\to (0,1)^{K}} , where K ≥...

density function is f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 {\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}}...

respective σ {\displaystyle \sigma } -algebras Σ {\displaystyle \Sigma } and T . {\displaystyle \mathrm {T} .} A function f : X → Y {\displaystyle f:X\to...

logistic function shown in the first figure and defined by the formula: σ ( x ) = 1 1 + e − x = e x 1 + e x = 1 − σ ( − x ) . {\displaystyle \sigma (x)={\frac...

Six Sigma (6σ) is a set of techniques and tools for process improvement. It was introduced by American engineer Bill Smith while working at Motorola in...

a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models...

asymptotically faster than any computable function. The busy beaver function, Σ : N → N {\displaystyle \Sigma :\mathbb {N} \to \mathbb {N} } , is defined...

to the origin (zero point) Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to...

starvation/stationary phase sigma factor σ54 (RpoN) – the nitrogen-limitation sigma factor There are also anti-sigma factors that inhibit the function of sigma factors and...

{65}{756}}\sigma _{11}(n)+{\frac {691}{756}}\sigma _{5}(n)-{\frac {691}{3}}\sum _{0<k<n}\sigma _{5}(k)\sigma _{5}(n-k),}     where τ(n) is Ramanujan's function....

{\displaystyle V(x;\sigma ,\gamma )={\frac {\operatorname {Re} [w(z)]}{{\sqrt {2\pi }}\,\sigma }},} where Re[w(z)] is the real part of the Faddeeva function evaluated...

probability density function of f ( x , μ , σ 2 ) = 1 σ 2 π e − 1 2 ( x − μ σ ) 2 {\displaystyle f\left(x,\mu ,\sigma ^{2}\right)={\frac {1}{\sigma {\sqrt {2\pi...

k\times k} matrix Σ {\displaystyle {\boldsymbol {\Sigma }}} , such that the characteristic function of X {\displaystyle \mathbf {X} } is φ X ( u ) = exp...

density function of the Rayleigh distribution is f ( x ; σ ) = x σ 2 e − x 2 / ( 2 σ 2 ) , x ≥ 0 , {\displaystyle f(x;\sigma )={\frac {x}{\sigma ^{2}}}e^{-x^{2}/(2\sigma...

In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function defined as: erf ⁡ z = 2 π ∫ 0 z e − t 2...

Sigma }_{11}^{x}&{\Sigma }_{12}^{x}&{\Sigma }_{13}^{x}&\cdots \\{\Sigma }_{21}^{x}&{\Sigma }_{22}^{x}&{\Sigma }_{23}^{x}&\cdots \\{\Sigma }_{31}^{x}&{\Sigma...