Expansion of

Navaza, J.

doi:10.1107/97809553602060000682

International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

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International Tables for Crystallography (2006). Vol. F. ch. 13.2, p. 274

Section A13.2.1.5. Expansion of $[\exp (2\pi i{\bf sr})]$

J. Navaza^a ^*

^aLaboratoire de Génétique des Virus, CNRS-GIF, 1. Avenue de la Terrasse, 91198 Gif-sur-Yvette, France
Correspondence e-mail: jnavaza@pasteur.fr

A13.2.1.5. Expansion of $[\exp (2\pi i{\bf sr})]$

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This is also called the plane-wave expansion or Laplace's expansion (Landau & Lifschitz, 1972): $[\exp (2\pi i{\bf sr}) = 4\pi {\textstyle\sum\limits_{\ell = 0}^{\infty}} i^{\ell} {\textstyle\sum\limits_{m = -\ell}^{\ell}} j_{\ell}(2\pi sr) \overline{Y_{\ell, \, m}({\hat {\bf s}})} Y_{\ell, \, m}({\hat {\bf r}}). \eqno(\hbox{A}13.2.1.15)]$

References

Landau, L. D. & Lifschitz, E. M. (1972). Théorie quantique relativiste, pp. 109–196. Moscow: Editions MIR.Google Scholar

International Tables for Crystallography (2006). Vol. F. ch. 13.2, p. 274