IJPAM: Volume 43, No. 4 (2008)
Department of Mathematics
201 Mullica Hill Road, Glassboro, NJ 08028-1701, USA
Abstract.The classical Lambert's series makes it possible to generate many remarkable transformations of series. These Lambert's series are all constructed from the function . In this paper we show how to generalize these series by using an arbitrary function in place of . Series transformations exhibiting beautiful symmetry are obtained. In addition, a double contour integral is found which represents these series. Our method is compared to a general procedure introduced by MacMahon.
Received: December 6, 2007
AMS Subject Classification: 30B10, 30B50, 30E20, 40A05, 40A30
Key Words and Phrases: Lambert's series, series transformations, contour integrals, numerical functions
Source: International Journal of Pure and Applied Mathematics