Euler's formula (redirect from E^ix=cos(x)+i*sin(x))
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...
26 KB (3,851 words) - 07:05, 26 September 2024
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...
21 KB (1,878 words) - 19:55, 12 August 2024
Fresnel integral (redirect from S(x))
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...
21 KB (2,649 words) - 05:23, 18 July 2024
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 >=...
20 KB (4,095 words) - 21:00, 8 April 2024
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...
10 KB (1,839 words) - 00:48, 21 July 2024
Binomial coefficient (redirect from N choose k)
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...
61 KB (10,608 words) - 16:11, 8 October 2024
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...
33 KB (5,759 words) - 18:51, 30 September 2024
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...
13 KB (2,449 words) - 16:51, 8 September 2024
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...
55 KB (10,413 words) - 14:13, 1 September 2024