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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.

A polynomial form which is the sum of two polynomial forms involving separate sets of variables.

Not continuous. A point at which a function is discontinuous is called a discontinuity, or sometimes a jump.

Johnson solid J_(90).

If lim_(k->infty)u_k!=0, then the series {u_n} diverges.

A divergent sequence is a sequence that is not convergent.

When ac is divisible by a number b that is relatively prime to a, then c must be divisible by b.

The star polygon {12/5}.

Distinguish between smooth manifolds in four dimensions.