%0 Journal Article %T On a class of generalized analytic functions %A Shyam L. Kalla %A Nina Virchenko %A Iryna Alexsandrovich %J Le Matematiche %D 2012 %I University of Catania %X 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. %K p-wave function %K Integral representation %K Inversion formula %K Cauchy problem %K Hankel transform %U http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/987