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The Hermite polynomials H_n(x) are set of orthogonal polynomials over the domain (-infty,infty) with weighting function e^(-x^2), illustrated above for n=1, 2, 3, and 4. ...

An alternating knot is a knot which possesses a knot diagram in which crossings alternate between under- and overpasses. Not all knot diagrams of alternating knots need be ...

Let n be a positive nonsquare integer. Then Artin conjectured that the set S(n) of all primes for which n is a primitive root is infinite. Under the assumption of the ...

The number obtained by adding the reciprocals of the odd twin primes, B=(1/3+1/5)+(1/5+1/7)+(1/(11)+1/(13))+(1/(17)+1/(19))+.... (1) By Brun's theorem, the series converges ...

The Petersen graph is the cubic graph on 10 vertices and 15 edges which is the unique (3,5)-cage graph (Harary 1994, p. 175), as well as the unique (3,5)-Moore graph. It can ...

The Taniyama-Shimura conjecture, since its proof now sometimes known as the modularity theorem, is very general and important conjecture (and now theorem) connecting topology ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

The Kronecker symbol is an extension of the Jacobi symbol (n/m) to all integers. It is variously written as (n/m) or (n/m) (Cohn 1980; Weiss 1998, p. 236) or (n|m) (Dickson ...

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...