GENERALIZED BESSEL-FUNCTIONS IN INCOMMENSURATE STRUCTURE-ANALYSIS

The analysis of incommensurate structures is computationally more diff icult than that of normal ones. This is mainly a result of the structu re-factor expression, which involves numerical integrations or infinit e series of Bessel functions. Both approaches have been implemented in existing computer programs. Compact analytical expressions are known for special cases only. Recently, a new theory of generalized Bessel f unctions has been developed. The number of theoretical results and app lications is increasing rapidly. Numerical properties and algorithms a re being studied. A possible application of the generalized Bessel fun ctions for incommensurate structure analysis is proposed. These functi ons can be used to derive analytical expressions for structure factors and all partial derivatives for a wide class of incommensurate crysta ls. The existing programs can be improved by taking into account some interesting numerical and analytical properties of these new functions , like recurrence relations, analytical expressions for derivatives, g enerating functions and integral representations. A new class of speci al functions, suitable for dealing with incommensurate structures in a more analytical way, is emerging.