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...

concept form named Vision iNext at the 2018 Paris Motor Show, and then as fully production-ready in November 2020. The iX is the first purpose-built...

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...

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 >=...

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...

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...

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...

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...

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 + ⋱...

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...