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Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...

The triangle DeltaA^*B^*C^* obtained by reflecting the vertices of a reference triangle DeltaABC about the opposite sides is called the reflection triangle (Grinberg 2003). ...

Given the closed interval [0,x] with x>1, let one-dimensional "cars" of unit length be parked randomly on the interval. The mean number M(x) of cars which can fit (without ...

The rising factorial x^((n)), sometimes also denoted <x>_n (Comtet 1974, p. 6) or x^(n^_) (Graham et al. 1994, p. 48), is defined by x^((n))=x(x+1)...(x+n-1). (1) This ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

A sequence s_n(x) is called a Sheffer sequence iff its generating function has the form sum_(k=0)^infty(s_k(x))/(k!)t^k=A(t)e^(xB(t)), (1) where A(t) = A_0+A_1t+A_2t^2+... ...

The most common "sine integral" is defined as Si(z)=int_0^z(sint)/tdt (1) Si(z) is the function implemented in the Wolfram Language as the function SinIntegral[z]. Si(z) is ...

A method for finding recurrence relations for hypergeometric polynomials directly from the series expansions of the polynomials. The method is effective and easily ...