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The power polynomials x^n are an associated Sheffer sequence with f(t)=t, (1) giving generating function sum_(k=0)^inftyx^kt^k=1/(1-tx) (2) and exponential generating ...

That portion of mathematics dealing with functions of real variables. While this includes some portions of topology, it is most commonly used to distinguish that portion of ...

An operator E such that E^ap(x)=p(x+a).

An operator T which maps some basic polynomial sequence p_n(x) into another basic polynomial sequence q_n(x).

The proof theories of propositional calculus and first-order logic are often referred to as classical logic. Intuitionistic propositional logic can be described as classical ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

The term "pathological" is used in mathematics to refer to an example specifically cooked up to violate certain almost universally valid properties. Pathological problems ...

The problem in calculus of variations to find the minimal surface of a boundary with specified constraints (usually having no singularities on the surface). In general, there ...