Four-term recurrence relations for hypergeometric functions of the second order. I (Q1915573)

The authors \textit{R. J. Yañez, J. Dehesa}, and \textit{A. Zarzo} [Nuovo Cimento B11, 109, No. 7, 725-733 (1994)] have discussed certain four term recurrence relations for hypergeometric functions from the point of view of their associated differential equations. In this paper, four term recurrence relations for hypergeometric functions of the second order are deduced from generating functions involving elementary functions. Generalizations are also given and an example is given of a five term recurrence relation for the confluent hypergeometric function. Series manipulation technique is used in this paper.