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Let (a)_i be a sequence of complex numbers and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as f_(nk)=(product_(j=k)^(n-1)(a_j+k))/((n-k)!) and ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

Let sumu_k be a series with positive terms and let f(x) be the function that results when k is replaced by x in the formula for u_k. If f is decreasing and continuous for ...

The composition quotient groups belonging to two composition series of a finite group G are, apart from their sequence, isomorphic in pairs. In other words, if I subset H_s ...

The kei_nu(z) function is defined as the imaginary part of e^(-nupii/2)K_nu(ze^(pii/4))=ker_nu(z)+ikei_nu(z), (1) where K_nu(z) is a modified Bessel function of the second ...

The symbol ker has at least two different meanings in mathematics. It can refer to a special function related to Bessel functions, or (written either with a capital or ...

An integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of ...

A lozenge (or rhombus) algorithm is a class of transformation that can be used to attempt to produce series convergence improvement (Hamming 1986, p. 207). The best-known ...

A Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. Any nilpotent Lie algebra is also solvable. The basic example of a nilpotent Lie ...

A Lie algebra g is solvable when its Lie algebra commutator series, or derived series, g^k vanishes for some k. Any nilpotent Lie algebra is solvable. The basic example is ...