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then (1.2) may be interpreted as a summability process which converts the generally divergent expansion (1.3) into a convergent expansion. If f(x) in (1.3) is of hypergeometric type,* then the coefficients bn (X) may be found formally at least using the procedures [5, 6]. These yield for bn(X) an asymptotic series in X which is also of hypergeometric type. The asymptotic representation for bn(N) in general is not suitable for computation. We are confronted with two problems: one is the interpretatiorn of the asymptotic series for bn (X), and the other is the computation of bn (N). In this paper, we show how both problems can be solved for a confluent hypergeometric function. Actually we derive a representation for bn(N) when f(x) is the G-function, which includes the confluent hypergeometric function as a special case. Our computational scheme for bn(X) is exhibited only when f(x) is a confluent hypergeometric function, although the ideas involved can be extended to cover other special cases of the G-function as well. In Section II, we prove an expansion theorem of the form (1.2) when f(x) is the

Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray