statistics, the Q-function is the tail distribution function of the standard normal distribution. In other words, Q ( x ) {\displaystyle Q(x)} is the probability...

given infinite exploration time and a partly random policy. "Q" refers to the function that the algorithm computes: the expected reward—that is, the...

In statistics, the generalized Marcum Q-function of order ν {\displaystyle \nu } is defined as Q ν ( a , b ) = 1 a ν − 1 ∫ b ∞ x ν exp ⁡ ( − x 2 + a 2...

minimax approximation or bound for the closely related Q-function: Q(x) ≈ Q̃(x), Q(x) ≤ Q̃(x), or Q(x) ≥ Q̃(x) for x ≥ 0. The coefficients {(an,bn)}N n = 1 for...

distribution functions F and G, with associated quantile functions F−1 and G−1 (the inverse function of the CDF is the quantile function), the Q–Q plot draws...

In probability and statistics, the quantile function is a function Q : [ 0 , 1 ] ↦ R {\displaystyle Q:[0,1]\mapsto \mathbb {R} } which maps some probability...

if and only if p ( x ) ≤ q ( x ) {\displaystyle p(x)\leq q(x)} for all x ∈ X . {\displaystyle x\in X.} A sublinear function is called minimal if it is...

sense that lim q → 1 ( q x ; q ) n ( 1 − q ) n = ( x ) n . {\displaystyle \lim _{q\to 1}{\frac {(q^{x};q)_{n}}{(1-q)^{n}}}=(x)_{n}.} The q-Pochhammer symbol...

In q-analog theory, the q {\displaystyle q} -gamma function, or basic gamma function, is a generalization of the ordinary gamma function closely related...

{\displaystyle V(s)} , the action-value Q-function Q ( s , a ) , {\displaystyle Q(s,a),} the advantage function A ( s , a ) {\displaystyle A(s,a)} , or...

Dirichlet function is the indicator function 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q {\displaystyle \mathbb {Q} } over...

Thomae's function is a real-valued function of a real variable that can be defined as:: 531  f ( x ) = { 1 q if  x = p q ( x  is rational), with  p ∈...

The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution...

Nowak, Robert (August 7, 2003). "The Q-function". Connexions. Barak, Ohad (April 6, 2006). "Q Function and Error Function" (PDF). Tel Aviv University. Archived...

eta function is defined as η ( z ) = q 1 / 24 ∏ n = 1 ∞ ( 1 − q n ) , q = e 2 π i z . {\displaystyle \eta (z)=q^{1/24}\prod _{n=1}^{\infty }(1-q^{n})...

function of n. If the ratio of successive terms is a rational function of qn, then the series is called a basic hypergeometric series. The number q is...

Nullwert function θ 3 ( q ) {\displaystyle \theta _{3}(q)} as this integral identity: θ 3 ( q ) = 1 + 4 q ln ⁡ ( 1 / q ) π ∫ 0 ∞ exp ⁡ [ − ln ⁡ ( 1 / q ) x...

the study of quantum effects in superconductors. The Husimi Q distribution (called Q-function in the context of quantum optics) is one of the simplest distributions...

n ) q n = q ∏ n ≥ 1 ( 1 − q n ) 24 = q ϕ ( q ) 24 = η ( z ) 24 = Δ ( z ) , {\displaystyle \sum _{n\geq 1}\tau (n)q^{n}=q\prod _{n\geq 1}\left(1-q^{n}\right)^{24}=q\phi...

gamma function. The Marcum Q-function Q M ( a , b ) {\displaystyle Q_{M}(a,b)} can also be used to represent the cdf. P ( x ; k , λ ) = 1 − Q k 2 ( λ...

Möbius function is ∑ n = 1 ∞ μ ( n ) q n 1 − q n = q , {\displaystyle \sum _{n=1}^{\infty }{\frac {\mu (n)q^{n}}{1-q^{n}}}=q,} which converges for | q | <...

Floor and ceiling functions In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer...

mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general...

In mathematics, the q-theta function (or modified Jacobi theta function) is a type of q-series which is used to define elliptic hypergeometric series...

In mathematics, a Jackson q-Bessel function (or basic Bessel function) is one of the three q-analogs of the Bessel function introduced by Jackson (1906a...

In algebra, a quartic function is a function of the formα f ( x ) = a x 4 + b x 3 + c x 2 + d x + e , {\displaystyle f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e,} where...

the Euler function is given by ϕ ( q ) = ∏ k = 1 ∞ ( 1 − q k ) , | q | < 1. {\displaystyle \phi (q)=\prod _{k=1}^{\infty }(1-q^{k}),\quad |q|<1.} Named...

P} and Q {\displaystyle Q} are polynomial functions of x {\displaystyle x} and Q {\displaystyle Q} is not the zero function. The domain of f {\displaystyle...

{(q^{a}+q^{2p-a})(q^{a+p}+q^{p-a})}{1-q^{3p}+{}}}\,{\frac {q^{p}(q^{a}+q^{3p-a})(q^{a+2p}+q^{p-a})}{1-q^{5p}+{}}}\,{\frac {q^{2p}(q^{a}+q^{4p-a})(q...

the function: F ( q , θ ) := E q ⁡ [ log ⁡ L ( θ ; x , Z ) ] + H ( q ) , {\displaystyle F(q,\theta ):=\operatorname {E} _{q}[\log L(\theta ;x,Z)]+H(q),}...