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Roman (1984, p. 26) defines "the" binomial identity as the equation p_n(x+y)=sum_(k=0)^n(n; k)p_k(y)p_(n-k)(x). (1) Iff the sequence p_n(x) satisfies this identity for all y ...

The join G=G_1+G_2 of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph union G_1 union G_2 together with all the edges joining ...

There are two sorts of transforms known as the fractional Fourier transform. The linear fractional Fourier transform is a discrete Fourier transform in which the exponent is ...

In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins. The Ising model in two dimensions is a type of ...

The term "(a,b)-leaper" (sometimes explicitly called a "single-pattern leaper") describes a fairy chess piece such as a knight that may make moves which simultaneously change ...

A maximal independent vertex set of a graph is an independent vertex set that cannot be expanded to another independent vertex set by addition of any vertex in the graph. A ...

A discrete function A(n,k) is called closed form (or sometimes "hypergeometric") in two variables if the ratios A(n+1,k)/A(n,k) and A(n,k+1)/A(n,k) are both rational ...

There are (at least) two mathematical constants associated with Theodorus. The first Theodorus's constant is the elementary algebraic number sqrt(3), i.e., the square root of ...

The polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z)=sum_(k=1)^infty(z^k)/(k^n) (1) defined in the complex plane over the open unit ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...