The asymptotic expansion of certain series considered by ramanujan

Abstract

Using the theory of generalized functions, the asymptotic expansion of a class of series of number theoretical importance is derived. The development of the corresponding Lambert type series as well as other multidimensional series expansions are obtained. The notion of a distributionally small sequence is intro¬duced and its relation with summability ideas is studied. Several illustrations are given

Keywords:

• Generalized functions
• asymptotic expansion
• arithmetical function
• Cesàro summability

AMS(MOS)::

• 41A60
• 46F12