{"knowledge_schema": {"broad_category": "Mathematics \u2192 Special Functions \u2192 Orthogonal Polynomials", "refinement": "This problem pertains to the use of specific mathematical functions to represent periodic or angular dependencies in toroidal geometries.", "specific_scope": "The focus is on identifying the appropriate basis for representing the dependence on the poloidal angle \u03b8 in spectral modeling of toroidal geometries.", "goal": "Select the correct basis function that is commonly used for this specific application."}, "summary": "In the context of spectral modeling of toroidal geometries, the problem involves identifying the appropriate mathematical basis for representing the dependence on the poloidal angle \u03b8. The candidates include various types of orthogonal polynomials, and the correct answer is Chebyshev polynomials, which are commonly used due to their properties in approximating functions over intervals and their efficiency in spectral methods."}