Limiting values of the Gegenbauer functions on the cut

Abstract

Limiting values and series representations of the Gegenbauer functions of the first and second kind of general complex degree ν and order λ on the cut (−1, 1) are presented. These limits are necessary for the analysis of certain boundary value problems associated with the theory of the potential and Stokes’ flow.

Keywords:

• Gegenbauer functions
• Legendre functions
• limiting values

AMS Subject Classification :

• 33C47
• 33C90