real number x, one has e i x = cos ⁡ x + i sin ⁡ x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary...

in concept form as the Vision iNext at the 2018 LA Auto Show, and then in its production form in November 2020. The iX is BMW's second fully electric...

function is ∫ x m e i x n d x = V n , m ( x ) e i x n , {\displaystyle \int x^{m}e^{ix^{n}}\,dx=V_{n,m}(x)e^{ix^{n}},} with V n , m := x m + 1 m + 1 1...

states that Var ⁡ ( ∑ i = 1 n X i ) = ∑ i = 1 n Var ⁡ ( X i ) + 2 ∑ i , j = 1 i < j n Cov ⁡ ( X i , X j ) = ∑ i , j = 1 n Cov ⁡ ( X i , X j ) {\displaystyle...

z n = x n + y n = x + y n x n − 1 + ( n − 1 ) y 2 x + ( n + 1 ) y 3 n x n − 1 + ( 2 n − 1 ) y 2 x + ( 2 n + 1 ) y 5 n x n − 1 + ( 3 n − 1 ) y 2 x + ⋱...

x ) {\displaystyle P(x)} of degree d {\displaystyle d} such that only certain derivatives have specified values at specified points: P ( n i ) ( x i )...

n ( x ) = e x n ! d n d x n ( e − x x n ) = 1 n ! ( d d x − 1 ) n x n , {\displaystyle L_{n}(x)={\frac {e^{x}}{n!}}{\frac {d^{n}}{dx^{n}}}\left(e^{-x...

scratch[ix - 1]); } x[ix] = (x[ix] - a[ix] * x[ix - 1]) / (b[ix] - a[ix] * scratch[ix - 1]); } /* loop from X - 2 to 0 inclusive */ for (int ix = X - 2; ix >=...

tightened to n 8 k ( n − k ) 2 n H ( k / n ) ≤ ( n k ) ≤ n 2 π k ( n − k ) 2 n H ( k / n ) {\displaystyle {\sqrt {\frac {n}{8k(n-k)}}}2^{nH(k/n)}\leq {n \choose...

_{i=1}^{n}\epsilon (X_{i})} or I ( X 1 ⊕ X 2 ⊕ ⋯ ⊕ X n ) = ∏ i = 1 n I ( X i ) {\displaystyle I(X_{1}\oplus X_{2}\oplus \cdots \oplus X_{n})=\prod _{i=1}^{n}I(X_{i})}...

x and integer n it is the case that ( cos ⁡ x + i sin ⁡ x ) n = cos ⁡ n x + i sin ⁡ n x , {\displaystyle {\big (}\cos x+i\sin x{\big )}^{n}=\cos nx+i\sin...

n 1 ∂ n 2 ) n 3 = ( ∂ n 1 n 3 ∂ n 2 n 3 ) n 3 = ( ∂ x 1 x 3 ∂ x 2 x 3 ) n 3 {\displaystyle \left({\frac {\partial n_{1}}{\partial n_{2}}}\right)_{n_{3}}=\left({\frac...

1 x 1 − x 0 x 1 ( x 1 − x 0 ) x 1 2 ( x 1 − x 0 ) ⋯ x 1 n − 1 ( x 1 − x 0 ) 1 x 2 − x 0 x 2 ( x 2 − x 0 ) x 2 2 ( x 2 − x 0 ) ⋯ x 2 n − 1 ( x 2 − x 0...

I + X k ) k {\displaystyle e^{X}=\lim _{k\rightarrow \infty }\left(I+{\frac {X}{k}}\right)^{k}} where I is the n×n identity matrix. When X is an n×n diagonal...

Massey as I ( X n → Y n ) = ∑ i = 1 n I ( X i ; Y i | Y i − 1 ) {\displaystyle I(X^{n}\to Y^{n})=\sum _{i=1}^{n}I(X^{i};Y_{i}|Y^{i-1})} , where X n {\displaystyle...

neighbourhood N {\displaystyle N} of x {\displaystyle x} there exists an integer i {\displaystyle i} with N i {\displaystyle N_{i}} contained in N . {\displaystyle...

_{i=1}^{n}\left|y_{i}-x_{i}\right|}{n}}={\frac {\sum _{i=1}^{n}\left|e_{i}\right|}{n}}.} It is thus an arithmetic average of the absolute errors | e i |...

I(X^{n};Y^{n})=I(X^{n}\to Y^{n})+I(Y^{n-1}\to X^{n}).} Two alternative forms of this law are I ( X n ; Y n ) = I ( X n → Y n ) + I ( Y n → X n ) − I ( X n ↔ Y n...

{1}{x-x_{i}}}} yields ∫ a b ω ( x ) x k p n ( x ) x − x i d x = x i k ∫ a b ω ( x ) p n ( x ) x − x i d x {\displaystyle \int _{a}^{b}\omega (x){\frac {x...

substantially from one another. x ¯ = C m + ∑ i = 1 n x i C + n {\displaystyle {\bar {x}}={Cm+\sum _{i=1}^{n}x_{i} \over C+n}} This is equivalent to adding...

∑ n = 0 ∞ a n ( x − c ) n = a 0 + a 1 ( x − c ) + a 2 ( x − c ) 2 + … {\displaystyle \sum _{n=0}^{\infty }a_{n}\left(x-c\right)^{n}=a_{0}+a_{1}(x...

+ x 6 + x 5 + x 4 + x 3 + x 2 + x + 1 Φ 12 ( x ) = x 4 − x 2 + 1 Φ 13 ( x ) = x 12 + x 11 + x 10 + x 9 + x 8 + x 7 + x 6 + x 5 + x 4 + x 3 + x 2 + x +...

eiX = cos X + i sin X, yielding sin ⁡ X = e i X − e − i X 2 i cos ⁡ X = e i X + e − i X 2 . {\displaystyle {\begin{aligned}\sin X&={e^{iX}-e^{-iX} \over...

a list of notable glamour models. Contents A B C D E F G H I J K L M N O P Q R S T U V W X Y Z List of pornographic performers by decade List of Playboy...

n x n + a n − 1 x n − 1 + ⋯ + a 0 = 0 {\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{0}=0} with integer coefficients a i ∈ Z {\displaystyle a_{i}\in...

scheme X of dimension n over a field k is a coherent sheaf ω X {\displaystyle \omega _{X}} together with a linear functional t X : H n ⁡ ( X , ω X ) → k...

many residue classes a i ( mod n i ) = { a i + n i x :   x ∈ Z } , {\displaystyle a_{i}{\pmod {n_{i}}}=\{a_{i}+n_{i}x:\ x\in \mathbb {Z} \},} whose union...

\sum _{i=1}^{n}w_{i}g(x_{i})} where x i = cos ⁡ ( i n + 1 π ) {\displaystyle x_{i}=\cos \left({\frac {i}{n+1}}\pi \right)} and the weight w i = π n + 1 sin...

i = p i ⋆ x i {\displaystyle p_{i}=p_{i}^{\star }x_{i}} where p i {\displaystyle p_{i}} is the partial pressure of the component i {\displaystyle i}...

( c i + ∑ j = 1 n ( x j − a i j ) 2 ) − 1 {\displaystyle f(x_{1},x_{2},...,x_{n-1},x_{n})=\sum _{i=1}^{m}\;\left(c_{i}+\sum \limits _{j=1}^{n}(x...