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Let the divisor function d(n) be the number of divisors of n (including n itself). For a prime p, d(p)=2. In general, sum_(k=1)^nd(k)=nlnn+(2gamma-1)n+O(n^theta), where gamma ...

Conditions at an initial time t=t_0 from which a given set of mathematical equations or physical system evolves. A system with initial conditions specified is known as an ...

Conditions arising in the study of the Robbins axiom and its connection with Boolean algebra. Winkler studied Boolean conditions (such as idempotence or existence of a zero) ...

Second and higher derivatives of the metric tensor g_(ab) need not be continuous across a surface of discontinuity, but g_(ab) and g_(ab,c) must be continuous across it.

Partial differential equation boundary conditions which give the normal derivative on a surface.

Partial differential equation boundary conditions which, for an elliptic partial differential equation in a region Omega, specify that the sum of alphau and the normal ...

If g is continuous and mu,nu>0, then int_0^t(t-xi)^(mu-1)dxiint_0^xi(xi-x)^(nu-1)g(xi,x)dx =int_0^tdxint_x^t(t-xi)^(mu-1)(xi-x)^(nu-1)g(xi,x)dxi.

Let |sum_(n=1)^pa_n|<K, (1) where K is independent of p. Then if f_n>=f_(n+1)>0 and lim_(n->infty)f_n=0, (2) it follows that sum_(n=1)^inftya_nf_n (3) converges.

If, in an interval of x, sum_(r=1)^(n)a_r(x) is uniformly bounded with respect to n and x, and {v_r} is a sequence of positive non-increasing quantities tending to zero, then ...

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...