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601 | 601 | ] |
602 | 602 | ] |
603 | 603 | >>> typst |
604 | | -upright("Bernoulli Trials") & P \( E \) = (n / k) p_()^k \( 1 - p \)_()^(n - k)\ |
| 604 | +upright("Bernoulli Trials") & P\(E\) = (n / k) p_()^k\(1 - p\)_()^(n - k)\ |
605 | 605 | upright("Cauchy-Schwarz Inequality") & (sum_(k = 1)^n a_k^() b_k^())_()^2 lt.eq (sum_(k = 1)^n a_k^2) (sum_(k = 1)^n b_k^2)\ |
606 | | -upright("Cauchy Formula") & f \( z \) thin dot.c "Ind"_gamma^() \( z \) = frac(1, 2 pi i) integral.cont_gamma^() frac(f \( xi \), xi - z) thin d xi\ |
| 606 | +upright("Cauchy Formula") & f\(z\)thin dot.c "Ind"_gamma^()\(z\)= frac(1, 2 pi i) integral.cont_gamma^() frac(f\(xi\), xi - z) thin d xi\ |
607 | 607 | upright("Cross Product") & V_1^() times V_2^() = mat(delim: "|", i, j, k; frac(partial X, partial u), frac(partial Y, partial u), 0; frac(partial X, partial v), frac(partial Y, partial v), 0)\ |
608 | | -upright("Vandermonde Determinant") & mat(delim: "|", 1, 1, dots.h.c, 1; v_1^(), v_2^(), dots.h.c, v_n^(); v_1^2, v_2^2, dots.h.c, v_n^2; dots.v, dots.v, dots.down, dots.v; v_1^(n - 1), v_2^(n - 1), dots.h.c, v_n^(n - 1)) = product_(1 lt.eq i < j lt.eq n)^() \( v_j^() - v_i^() \)\ |
609 | | -upright("Lorenz Equations") & accent(x, ˙)_() & = & sigma \( y - x \)\ |
| 608 | +upright("Vandermonde Determinant") & mat(delim: "|", 1, 1, dots.h.c, 1; v_1^(), v_2^(), dots.h.c, v_n^(); v_1^2, v_2^2, dots.h.c, v_n^2; dots.v, dots.v, dots.down, dots.v; v_1^(n - 1), v_2^(n - 1), dots.h.c, v_n^(n - 1)) = product_(1 lt.eq i < j lt.eq n)^()\(v_j^() - v_i^()\)\ |
| 609 | +upright("Lorenz Equations") & accent(x, ˙)_() & = & sigma\(y - x\)\ |
610 | 610 | accent(y, ˙)_() & = & rho x - y - x z\ |
611 | 611 | accent(z, ˙)_() & = & - beta z + x y\ |
612 | 612 | upright("Maxwell's Equations") & {nabla zws times accent(B, ↼)_() - thin 1 / c thin frac(partial zws accent(E, ↼)_(), partial zws t) & = & frac(4 pi, c) thin accent(j, ↼)_()\ |
613 | 613 | nabla zws dot.c accent(E, ↼)_() & = & 4 pi rho\ |
614 | 614 | nabla zws times accent(E, ↼)_() thin + thin 1 / c thin frac(partial zws accent(B, ↼)_(), partial zws t) & = & accent(0, ↼)_()\ |
615 | 615 | nabla zws dot.c accent(B, ↼)_() & = & 0\ |
616 | 616 | upright("Einstein Field Equations") & R_(mu nu)^() - 1 / 2 thin g_(mu nu)^() thin R = frac(8 pi G, c_()^4) thin T_(mu nu)^()\ |
617 | | -upright("Ramanujan Identity") & frac(1, \( sqrt(phi sqrt(5)) - phi \) e_()^(25 / pi)) = 1 + frac(e_()^(- 2 pi), 1 + frac(e_()^(- 4 pi), 1 + frac(e_()^(- 6 pi), 1 + frac(e_()^(- 8 pi), 1 + dots.h))))\ |
| 617 | +upright("Ramanujan Identity") & frac(1, \(sqrt(phi sqrt(5)) - phi\)e_()^(25 / pi)) = 1 + frac(e_()^(- 2 pi), 1 + frac(e_()^(- 4 pi), 1 + frac(e_()^(- 6 pi), 1 + frac(e_()^(- 8 pi), 1 + dots.h))))\ |
618 | 618 | upright("Another Ramanujan identity") & sum_(k = 1)^oo 1 / 2_()^(floor.l k dot.c zws phi floor.r) = frac(1, 2_()^0 + frac(1, 2_()^1 + dots.h.c))\ |
619 | | -upright("Rogers-Ramanujan Identity") & 1 + sum_(k = 1)^oo frac(q_()^(k_()^2 + k), \( 1 - q \) \( 1 - q_()^2 \) dots.h.c \( 1 - q_()^k \)) = product_(j = 0)^oo frac(1, \( 1 - q_()^(5 j + 2) \) \( 1 - q_()^(5 j + 3) \)) \, upright(" ") upright(" ") f o r med \| q \| < 1 .\ |
| 619 | +upright("Rogers-Ramanujan Identity") & 1 + sum_(k = 1)^oo frac(q_()^(k_()^2 + k), \(1 - q\)\(1 - q_()^2\)dots.h.c\(1 - q_()^k\)) = product_(j = 0)^oo frac(1, \(1 - q_()^(5 j + 2)\)\(1 - q_()^(5 j + 3)\))\,upright(" ") upright(" ") f o r med\|q\|< 1 .\ |
620 | 620 | upright("Commutative Diagram") & H & arrow.l & K\ |
621 | 621 | arrow.b & zws & arrow.t\ |
622 | 622 | H & arrow.r & K |
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