On Hypergeometric Functions in Iterated Networks

Application of hypergeometric functions to analysis of linear, cascaded, identical fourpoles is investigated. Expressions for iterated network functions are derived in terms of this class of functions. Cascaded, isolated, singular fourpoles are examined in terms of the confluent hypergeometric function of several variables. Examples demonstrate how this function reduces to several special functions which are also useful in treating more general iterated networks. The Chebyshev polynomials and another hypergeometric function, called here the Jacobi-Chebyshev function, are used to analyze passive iterated networks. Extensions of the method lead to compound functions of hypergeometric functions. Expressions for current and voltage in transmission lines as a limiting case of infinitesimal fourpoles, together with an example of their application, are also included.