On a class of generalized analytic functions

Abstract

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.

Keywords

• p-wave function
• Integral representation
• Inversion formula
• Cauchy problem
• Hankel transform