An eigenfunction is a type of eigenvector. It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. Then formula 70 is an eigenfunction of formula 71 with eigenvalue 0. In this case the eigenfunction is itself a function of its associated eigenvalue. That is, "g"("x") is an eigenfunction of Bernoulli transfer operator, with eigenvalue "f"("k"). So formula 45 is an eigenfunction of the Hamiltonian. In particular, the standard normal distribution formula 48 is an eigenfunction of the Fourier transform. The main eigenfunction article gives other examples. A refinable function is an eigenfunction of that operator. The function "e" is thus an eigenfunction of the Weierstrass transform. His high frequency eigenfunction calculations are some of the fastest in the world.