On a class of generalized analytic functions

This paper deals with a new generalization of analytical functions. The p-wave functions are introduced and studied. We consider their theoretical aspect and applications. Some integral representations of x^k y^l -wave functions (k, l const. > 0), and their inversion formulas are derived. As an application of the theory, a singular Cauchy problem is formulated and solved in terms of the Bessel function of the first kind and Gauss hypergeometric function.