PN

Pn is a notation used across multiple disciplines to denote a family of objects indexed by the natural number n. Because meanings depend on context, Pn does not refer to a single universal concept.

In mathematics, Pn commonly denotes the space of polynomials in one variable of degree at most n, often written as Pn(F) for a field F. In graph theory, Pn denotes the path graph on n vertices, a simple chain of vertices connected by n−1 edges. In analysis and mathematical physics, Pn(x) frequently represents the nth Legendre polynomial, a standard orthogonal polynomial on the interval [-1, 1].

In geometry and topology, projective n-space is usually written P^n rather than Pn, with the superscript emphasizing the dimension; some older texts may omit the superscript and use Pn in informal contexts.

In other contexts, Pn appears as a generic index for a family of objects, such as a sequence of objects P1, P2, P3, and so on, with definitions supplied within a given work. In statistics or probability, Pn can be used to denote particular probabilities, percentiles, or predictive quantities, depending on the author’s conventions.

Because Pn spans several fields, readers should rely on the specific definitions provided in a given source to avoid ambiguity.