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A function which has infinitely many derivatives at a point. If a function is not polygenic, it is monogenic.

The contravariant four-vector arising in special and general relativity, x^mu=[x^0; x^1; x^2; x^3]=[ct; x; y; z], (1) where c is the speed of light and t is time. ...

Let A be a C^*-algebra, then a linear functional f on A is said to be positive if it is a positive map, that is f(a)>=0 for all a in A_+. Every positive linear functional is ...

Let A and B be C^*-algebras, then a linear map phi:A->B is said to be positive if phi(A_+) subset= B_+. Here, A_+ is denoted the positive part of A. For example, every ...

The positive real axis is the portion of the real axis with x>0.

The term used in physics and engineering for a harmonic function. Potential functions are extremely useful, for example, in electromagnetism, where they reduce the study of a ...

The study of harmonic functions (also called potential functions).

The algebra A is called a pre-C^*-algebra if it satisfies all conditions to be a C^*-algebra except that its norm need not be complete.

If a function f has a pole at z_0, then the negative power part sum_(j=-k)^(-1)a_j(z-z_0)^j (1) of the Laurent series of f about z_0 sum_(j=-k)^inftya_j(z-z_0)^j (2) is ...

A pseudoanalytic function is a function defined using generalized Cauchy-Riemann equations. Pseudoanalytic functions come as close as possible to having complex derivatives ...