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Two quantities are said to be different (or "unequal") if they are not equal. The term "different" also has a technical usage related to modules. Let a module M in an ...

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.

A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

delta(r)=sqrt(r)-2alpha(r), where alpha(r) is the elliptic alpha function.

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if lim_(x->infty)^_(e^xf(e^x))/(f(x))<1 and divergent if lim_(x->infty)__(e^xf(e^x))/(f(x))>1.

A line segment connecting nonadjacent polyhedron vertices sharing a common face in a parallelepiped or other similar solid.

For even h, (1) (Nagell 1951, p. 176). Writing out symbolically, sum_(n=0)^h((-1)^nproduct_(k=0)^(n-1)(1-x^(h-k)))/(product_(k=1)^(n)(1-x^k))=product_(k=0)^(h/2-1)1-x^(2k+1), ...

A polynomial that represents integers for all integer values of the variables. An integer polynomial is a special case of such a polynomial. In general, every integer ...

The Lebesgue identity is the algebraic identity (Nagell 1951, pp. 194-195).

A lens space L(p,q) is the 3-manifold obtained by gluing the boundaries of two solid tori together such that the meridian of the first goes to a (p,q)-curve on the second, ...