Orthogonal (series)

In mathematics, particularly in the fields of functional analysis and Fourier analysis, the term "orthogonal series" refers to a series of functions (or vectors) that are orthogonal to each other in a specified inner product space. 1. **Orthogonality**: Two functions (or vectors) \( f \) and \( g \) are considered orthogonal if their inner product (which may be defined as an integral, dot product, etc., depending on the context) is zero.