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(d^2u)/(dz^2)+(du)/(dz)+(k/z+(1/4-m^2)/(z^2))u=0. (1) Let u=e^(-z/2)W_(k,m)(z), where W_(k,m)(z) denotes a Whittaker function. Then (1) becomes ...

A variant of the Pollard p-1 method which uses Lucas sequences to achieve rapid factorization if some factor p of N has a decomposition of p+1 in small prime factors.

Begin with the Yff central triangle and then parallel-displace the isoscelizers in such a way as to reduce the central triangle to a point while keeping the other three ...

A Z-number is a real number xi such that 0<=frac[(3/2)^kxi]<1/2 for all k=1, 2, ..., where frac(x) is the fractional part of x. Mahler (1968) showed that there is at most one ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

Calculus II

The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

The de Longchamps circle is defined as the radical circle of the power circles of a given reference triangle. It is defined only for obtuse triangles. It is the complement of ...

A k-subset is a subset of a set on n elements containing exactly k elements. The number of k-subsets on n elements is therefore given by the binomial coefficient (n; k). For ...

Define the nome by q=e^(-piK^'(k)/K(k))=e^(ipitau), (1) where K(k) is the complete elliptic integral of the first kind with modulus k, K^'(k)=K(sqrt(1-k^2)) is the ...