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To compute an integral of the form int(dx)/(a+bx+cx^2), (1) complete the square in the denominator to obtain int(dx)/(a+bx+cx^2)=1/cint(dx)/((x+b/(2c))^2+(a/c-(b^2)/(4c^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 ...

Any system of phi(n) integers, where phi(n) is the totient function, representing all the residue classes relatively prime to n is called a reduced residue system (Nagell ...

In a complete metric space, a countable union of nowhere dense sets is said to be meager; the complement of such a set is a residual set.

The direct product of the rings R_gamma, for gamma some index set I, is the set product_(gamma in I)R_gamma={f:I-> union _(gamma in I)R_gamma|f(gamma) in R_gamma all gamma in ...

Deciding whether a given Boolean formula in conjunctive normal form has an assignment that makes the formula "true." In 1971, Cook showed that the problem is NP-complete.

Every dense linear order complete set without endpoints having at most omega disjoint intervals is order isomorphic to the continuum of real numbers, where omega is the set ...

Let (K,|·|) be a complete non-Archimedean valuated field, with valuation ring R, and let f(X) be a power series with coefficients in R. Suppose at least one of the ...

The space join of a topological space X and a pair of points S^0, Sigma(X)=X*S^0.

Let E be a linear space over a field K. Then the vector space tensor product tensor _(lambda=1)^(k)E is called a tensor space of degree k. More specifically, a tensor space ...