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For all integers n and |x|<a, lambda_n^((t))(x+a)=sum_(k=0)^infty|_n; k]lambda_(n-k)^((t))(a)x^k, where lambda_n^((t)) is the harmonic logarithm and |_n; k] is a Roman ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

The triangular snake graph TS_n is the graph on n vertices with n odd defined by starting with the path graph P_(n-1) and adding edges (2i-1,2i+1) for i=1, ..., n-1. The ...

Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals," which are numbers that are ...

A cubic vertex-transitive graph is a cubic graph that is vertex transitive. Read and Wilson (1998, pp. 161-163) enumerate all connected cubic vertex-transitive graphs on 34 ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

The doubly truncated Witt graph is the graph on 330 vertices related to a 3-(22,8,12) design (Brouwer et al. 1989, p. 367). The doubly truncated Witt graph can be constructed ...

Let the elliptic modulus k satisfy 0<k^2<1, and the Jacobi amplitude be given by phi=amu with -pi/2<phi<pi/2. The incomplete elliptic integral of the first kind is then ...