# The orientational average of exp2i(h.x + k.y + l.z)

The orientational average of exp2i(h.x + k.y + l.z) The unit vectors el, e2, e3 form a fixed orthogonal coordinate frame. The unit vectors el', e2', e3' form a movable orthogonal frame with the same origin as the fixed frame. All orientations in space of the movable frame are assumed to be equally probable. Under these conditions the average of exp 2i(3i,j = 1aijei.e'j) is calculated. As an application the average of exp 2i(h.x + k.y + l.z) is calculated where the vectors h,k,l are specified and where the magnitudes of the vectors x,y,z and the angles between them are specified. This integral is of importance in utilizing a priori knowledge of molecular structure as an aid in solving the phase problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography International Union of Crystallography

# The orientational average of exp2i(h.x + k.y + l.z)

, Volume 34 (6): 955 – Nov 1, 1978

## The orientational average of exp2i(h.x + k.y + l.z)

, Volume 34 (6): 955 – Nov 1, 1978

### Abstract

The unit vectors el, e2, e3 form a fixed orthogonal coordinate frame. The unit vectors el', e2', e3' form a movable orthogonal frame with the same origin as the fixed frame. All orientations in space of the movable frame are assumed to be equally probable. Under these conditions the average of exp 2i(3i,j = 1aijei.e'j) is calculated. As an application the average of exp 2i(h.x + k.y + l.z) is calculated where the vectors h,k,l are specified and where the magnitudes of the vectors x,y,z and the angles between them are specified. This integral is of importance in utilizing a priori knowledge of molecular structure as an aid in solving the phase problem.

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Publisher
International Union of Crystallography
Copyright (c) 1978 International Union of Crystallography
ISSN
0567-7394
DOI
10.1107/S0567739478001953
Publisher site
See Article on Publisher Site

### Abstract

The unit vectors el, e2, e3 form a fixed orthogonal coordinate frame. The unit vectors el', e2', e3' form a movable orthogonal frame with the same origin as the fixed frame. All orientations in space of the movable frame are assumed to be equally probable. Under these conditions the average of exp 2i(3i,j = 1aijei.e'j) is calculated. As an application the average of exp 2i(h.x + k.y + l.z) is calculated where the vectors h,k,l are specified and where the magnitudes of the vectors x,y,z and the angles between them are specified. This integral is of importance in utilizing a priori knowledge of molecular structure as an aid in solving the phase problem.

### Journal

Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General CrystallographyInternational Union of Crystallography

Published: Nov 1, 1978

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