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A ring for which the product of any pair of ideals is zero only if one of the two ideals is zero. All simple rings are prime.

The derivative identity d/(dx)[f(x)g(x)] = lim_(h->0)(f(x+h)g(x+h)-f(x)g(x))/h (1) = (2) = lim_(h->0)[f(x+h)(g(x+h)-g(x))/h+g(x)(f(x+h)-f(x))/h] (3) = f(x)g^'(x)+g(x)f^'(x), ...

The derivative rule d/(dx)[(f(x))/(g(x))]=(g(x)f^'(x)-f(x)g^'(x))/([g(x)]^2).

The two-argument Ramanujan function is defined by phi(a,n) = 1+2sum_(k=1)^(n)1/((ak)^3-ak) (1) = 1-1/a(H_(-1/a)+H_(1/a)+2H_n-H_(n-1/a)-H_(n+1/a)). (2) The one-argument ...

int_0^inftycos(2zt)sech(pit)dt=1/2sechz for |I[z]|<pi/2. A related integral is int_0^inftycosh(2zt)sech(pit)dt=1/2secz for |R[z]|<pi/2.

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z], is said to be Saalschützian if it is k-balanced with k=1, ...

A Greek cross rotated by 45 degrees, also called the crux decussata, illustrated schematically above in polyomino form. The multiplication sign × is based on Saint Andrew's ...

The Seiberg-Witten equations are D_Apsi = 0 (1) F_A^+ = -tau(psi,psi), (2) where tau is the sesquilinear map tau:W^+×W^+->Lambda^+ tensor C.

The surface given by the parametric equations x = asinu (1) y = asinv (2) z = asin(u+v). (3) It is a sextic surface with algebraic equation (4) The coefficients of the first ...

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).