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Generalized Spherical Functions of Cubic Symmetry
Author(s) -
Bunge H. J.,
Küttner K.
Publication year - 1974
Publication title -
kristall und technik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0023-4753
DOI - 10.1002/crat.19740090910
Subject(s) - homogeneous space , symmetry (geometry) , circular symmetry , series (stratigraphy) , orthorhombic crystal system , power series , cubic form , truncation (statistics) , texture (cosmology) , power function , spherical mean , function (biology) , order (exchange) , mathematics , cubic crystal system , mathematical analysis , symmetry group , pure mathematics , geometry , physics , condensed matter physics , diffraction , quantum mechanics , computer science , image (mathematics) , geology , paleontology , statistics , finance , artificial intelligence , evolutionary biology , economics , biology
In the three‐dimensional texture analysis generalized spherical functions of certain symmetries are being used in order to develop the texture function into a series. The lower order members of this series are closely related to the symmetry of physical properties of textured materials whereas the highest order ones allow the series truncation error and hence the angular resolving power to be estimated. These functions have been calculated and represented graphically for the most important cases of cubic‐cubic and cubic‐orthorhombic symmetries for 1 ≦ 10. Additionally some sections of these functions are given for 1 = 22.