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The Struve function, denoted H_n(z) or occasionally H_n(z), is defined as H_nu(z)=(1/2z)^(nu+1)sum_(k=0)^infty((-1)^k(1/2z)^(2k))/(Gamma(k+3/2)Gamma(k+nu+3/2)), (1) where ...

The traveling salesman problem is a problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian cycle a salesman can take through each of n ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

The Walsh functions consist of trains of square pulses (with the allowed states being -1 and 1) such that transitions may only occur at fixed intervals of a unit time step, ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an ...

A derangement is a permutation in which none of the objects appear in their "natural" (i.e., ordered) place. For example, the only derangements of {1,2,3} are {2,3,1} and ...

The divergence of a vector field F, denoted div(F) or del ·F (the notation used in this work), is defined by a limit of the surface integral del ·F=lim_(V->0)(∮_SF·da)/V (1) ...

A theorem sometimes called "Euclid's first theorem" or Euclid's principle states that if p is a prime and p|ab, then p|a or p|b (where | means divides). A corollary is that ...