A. I. Aptekarev, R. E. Akhmedov, V. S. Buyarov, “Representation of the Gauss-Babenko operator in the power series basis”, Keldysh Institute preprints, 2012,069, 23 pp.

Representation of the Gauss-Babenko operator in the power series basis

A. I. Aptekarev, R. E. Akhmedov, V. S. Buyarov

Abstract: Formal properties of the Gauss operator are considered. We give statement of the Gauss problem. An integral form of this operator (discovered before by K.I. Babenko) is derived. The representation of this operator in the power series basis is obtained.

Keywords: Number theory; Gauss–Kuzmin statistic; continued fraction.