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An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of ...

A generalization of the complete beta function defined by B(z;a,b)=int_0^zu^(a-1)(1-u)^(b-1)du, (1) sometimes also denoted B_z(a,b). The so-called Chebyshev integral is given ...

The "complete" gamma function Gamma(a) can be generalized to the incomplete gamma function Gamma(a,x) such that Gamma(a)=Gamma(a,0). This "upper" incomplete gamma function is ...

A function f(x) increases on an interval I if f(b)>=f(a) for all b>a, where a,b in I. If f(b)>f(a) for all b>a, the function is said to be strictly increasing. Conversely, a ...

An independent variable is a variable whose values don't depend on changes in other variables. This is in contrast to the definition of dependent variable. As with dependent ...

An indicial equation, also called a characteristic equation, is a recurrence equation obtained during application of the Frobenius method of solving a second-order ordinary ...

Given a sequence of real numbers a_n, the infimum limit (also called the limit inferior or lower limit), written lim inf and pronounced 'lim-inf,' is the limit of ...

At the age of 17, Bernard Mares proposed the definite integral (Borwein and Bailey 2003, p. 26; Bailey et al. 2006) C_2 = int_0^inftycos(2x)product_(n=1)^(infty)cos(x/n)dx ...

A real-valued univariate function f=f(x) is said to have an infinite discontinuity at a point x_0 in its domain provided that either (or both) of the lower or upper limits of ...

An inhomogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not ...