What is "eigenfunction"

n. (context mathematics English) A function $phi$ such that, for a given linear operator $D$, $Dphi=lambdaphi$ for some scalar $lambda$ (called an eigenvalue).

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written as

Df = λf
for some scalar eigenvalue λ. The solutions to this equation may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions.

An eigenfunction is a type of eigenvector.