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Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...

A tetrahedron having a trihedron all of the face angles of which are right angles. The face opposite the vertex of the right angles is called the base. If the edge lengths ...

A Heronian triangle is a triangle having rational side lengths and rational area. The triangles are so named because such triangles are related to Heron's formula ...

The area of a surface or lamina is the amount of material needed to "cover" it completely. The area of a surface or collection of surfaces bounding a solid is called, not ...

In his famous paper of 1859, Riemann stated that the number N(T) of Riemann zeta function zeros sigma+it with 0<t<=T is asymptotically given by ...

An expression which is a sentence or which contains variables and becomes a sentence upon appropriate substitutions for these variables (Carnap 1958, p. 24). Sentential ...

D^*Dpsi=del ^*del psi+1/4Rpsi-1/2F_L^+(psi), where D is the Dirac operator D:Gamma(W^+)->Gamma(W^-), del is the covariant derivative on spinors, R is the scalar curvature, ...

Let alpha be a nonzero rational number alpha=+/-p_1^(alpha_1)p_2^(alpha_2)...p_L^(alpha_L), where p_1, ..., p_L are distinct primes, alpha_l in Z and alpha_l!=0. Then ...

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.

Slater (1960, p. 31) terms the identity _4F_3[a,1+1/2a,b,-n; 1/2a,1+a-b;1+a+n]=((1+a)_n(1/2+1/2a-b)_n)/((1/2+1/2a)_n(1+a-b)_n) for n a nonnegative integer the "_4F_3[1] ...