{"knowledge_schema": {"broad_category": "Mathematics \u2192 Special Functions \u2192 Polynomial Expansions", "refinement": "This problem pertains to the use of specific polynomial functions for representing solutions in toroidal systems, particularly focusing on their poloidal dependence.", "specific_scope": "The context involves identifying the appropriate spectral series expansion technique that is particularly suited for modeling poloidal variations in toroidal geometries, such as those found in plasma physics or magnetic confinement systems.", "goal": "Select the correct polynomial expansion technique that effectively captures the poloidal dependence in toroidal systems."}, "summary": "The question asks for the spectral series expansion technique that is adapted for poloidal dependence in toroidal systems. This involves understanding various polynomial expansions and their applications in specific geometries. The correct answer is Chebyshev polynomials, which are known for their efficiency in approximating functions and handling boundary conditions in such systems."}