Features of Constructing a Solution Heterogeneous Equation and Clausen-Type Systems

The possibilities of constructing a solution to an inhomogeneous the third-order equation have been studied, in particular Clausen vicinity special points x=0 and x=∞. construction method for indeterminate coefficients partial solutions is shown. These ideas are extended private simple system near regular feature with form product two hypergeometric functions, each which depends on one variable. A number properties functions constructed these features proved. common main heterogeneous investigated. Four new created, representing systems like Clausen.