International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 41

The previous results now allow a selfcontained and rigorous proof of the reciprocity theorem between and to be given, whereas in traditional settings (i.e. in and ) the implicit handling of δ through a limiting process is always the sticking point.
Reciprocity is first established in as follows:and similarly
The reciprocity theorem is then proved in by transposition:Thus the Fourier cotransformation in may legitimately be called the `inverse Fourier transformation'.
The method of Section 1.3.2.4.3 may then be used to show that and both have period 4 in .