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Abstract
In this paper the author finds the condition on b and c such that the incomplete beta function φ(b, c; z) defined by φ(b, c; z):=z
2
F
1(1, b; c; z) and the normalized confluent hypergeometric function are convex in Δ. Conditions on a, b, and c for the convexity of z
2
F
1(a, b; c; z) and z
1
F
1(a; c; z) for a≠1 remains an open problem.
Acknowledgements
This work was initiated when the author was in I.I.T. Madras, India in the DST Sponsored Research project (Ref. No. DST/MS/092/98). The author wishes to thank Dr.S.Ponnusamy for this problem and suggestions till this final form.