On the representational nonuniqueness of uniform waveguide eigenvalue formulas

It is found that, for uniform perfectly conducting waveguides characterized by rectilinear boundaries and exact eigenvalue formulas, such formulas are not representationally unique. They are specific examples of general homogeneous polynomials of degree p in q variables, known as q-ary, p-ic forms. Using the concepts of equivalence and congruence, it is found that an infinite number of eigenvalue formulas (that are members of an equivalence or congruence class) may be associated with a given waveguide cross-section.<
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