Decomposition of integrals of the some classes in generalized power series

Svetlana V. Savina

Financial University under the Government of the Russian Federation, Moscow, Russia

Abstract: It is investigated the decomposition of the Cauchy integrals the special kind in uniformly and absolutely converging generalized power series which it is possible to “differentiate” any number of times of the generalized derivative like the rule of differentiation by $z$ of usual power series. It is deduced the formulas for a finding of the generalized derivative.

Keywords: the analyticity, generalized power series, the generalized derivative.

UDC: 517.53

Received: 18.08.2010
Received in revised form: 25.10.2010
Accepted: 20.11.2010