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The Condon-Shortley phase is the factor of (-1)^m that occurs in some definitions of the spherical harmonics (e.g., Arfken 1985, p. 682) to compensate for the lack of ...

A confidence interval is an interval in which a measurement or trial falls corresponding to a given probability. Usually, the confidence interval of interest is symmetrically ...

The second-order ordinary differential equation xy^('')+(c-x)y^'-ay=0, sometimes also called Kummer's differential equation (Slater 1960, p. 2; Zwillinger 1997, p. 124). It ...

_0F_1(;a;z)=lim_(q->infty)_1F_1(q;a;z/q). (1) It has a series expansion _0F_1(;a;z)=sum_(n=0)^infty(z^n)/((a)_nn!) (2) and satisfies z(d^2y)/(dz^2)+a(dy)/(dz)-y=0. (3) It is ...

A constant function is function f(x)=c whose value does not change as its parameters vary. The function graph of a one-dimensional constant function is a straight line. The ...

A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological ...

A test to determine if a given series converges or diverges.

Let f(t) and g(t) be arbitrary functions of time t with Fourier transforms. Take f(t) = F_nu^(-1)[F(nu)](t)=int_(-infty)^inftyF(nu)e^(2piinut)dnu (1) g(t) = ...

The Cookson Hills series is the series similar to the Flint Hills series, but with numerator sec^2n instead of csc^2n: S_2=sum_(n=1)^infty(sec^2n)/(n^3) (Pickover 2002, p. ...

Let {a_n} be a nonnegative sequence and f(x) a nonnegative integrable function. Define A_n = sum_(k=1)^(n)a_k (1) B_n = sum_(k=n)^(infty)a_k (2) and F(x) = int_0^xf(t)dt (3) ...