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Let there be two particularly well-behaved functions F(x) and p_tau(x). If the limit lim_(tau->0)int_(-infty)^inftyp_tau(x)F(x)dx exists, then p_tau(x) is a regular sequence ...

An operator definition of a function. A Rodrigues formula may be converted into a Schläfli integral.

The Schur polynomials are a class of orthogonal polynomials. They are a special case of the Jack polynomials corresponding to the case alpha=1.

psi=(A_0+alpha_1A_1+alpha_2A_2+...)e^(iS/alpha).

Solving the wave equation on a disk gives a solution in terms of Bessel functions.

A function w(x) used to normalize orthogonal functions int[f_n(x)]^2w(x)dx=N_n.

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

Let {u_n(x)} be a sequence of functions. If 1. u_n(x) can be written u_n(x)=a_nf_n(x), 2. suma_n is convergent, 3. f_n(x) is a monotonic decreasing sequence (i.e., ...

The inequality sinAsinBsinC<=((3sqrt(3))/(2pi))^3ABC, where A, B, and C are the vertex angles of a triangle. The maximum is reached for an equilateral triangle (and therefore ...

If, for n>=0, beta_n=sum_(r=0)^n(alpha_r)/((q;q)_(n-r)(aq;q)_(n+r)), (1) then beta_n^'=sum_(r=0)^n(alpha_r^')/((q;q)_(n-r)(aq;q)_(n+r)), (2) where alpha_r^' = ...