A NEW LOOK AT q-HYPERGEOMETRIC FUNCTIONS

A NEW LOOK AT q-HYPERGEOMETRIC FUNCTIONS

For complex parameters ai, bj , q i = 1, ..., r, j = 1, ..., s, bj ∈ C\{0, −1, −2, ...}, |q|

___

  • Andrews,G.E., (1974), Applications of basic hypergeometric function, SIAM Review, vol. 16,no. 4, pp. 441-484.
  • Dziok, J., Srivastava,H.M., (1999), Classes of analytic functions associated with the generalized hy- pergeometric function, Applied Mathematics and Computation, vol. 103, pp. 1-13.
  • Exton,H., (1983),q-Hypergeometric functions and applications, Ellis Horwood Limited, Chichester, 347 pages.
  • Ghany, H.A., (2009), q-derivative of basic hypergeometric series with respect to parameters, Interna- tional Journal of Mathematical Analysis, vol. 3, no. 33, pp. 1617- 1632.
  • Frasin, B.A, Darus,M.,O (2001), On certain analytic univalent functions, International Journal of Mathematics and Mathematical Sciences, vol. 25, no. 5, pp. 305-310.
  • Ruscheweyh, S., (1975), New criteria for univalent functions, Proceedings of the American Mathemat- ical Society, vol. 49, pp. 109-115.
  • Mohammed, A., Darus,M., (2013), A generalized operator involving the q-hypergeometric function, Matematicki Vesnik. 65, 4, 454465.
  • Gasper, G., Rahman,M., (1990), Basic Hypergeometric Series , Encyclopedia of Mathematics and Its Application, Vol. 35, Cambridge University Press,Cambridge.
  • Carlson, B.C., Shaffer, D.B., (1984), Starlike and prestarlike hypergeometric functions, SIAM Journal on Mathematical Analysis, vol. 15, no. 4, pp. 737-745.
  • Bernardi, S.D., (1969), Convex and starlike univalent functions, Transactions of the American Math- ematical Society, vol. 135, pp. 429-446.
  • Libera, R.J., (1965), Some classes of regular univalent functions, Proceedings of the American Math- ematical Society, vol. 16, pp. 755-758.
  • Livingston,A.E., (1966), On the radius of univalence of certain analytic functions, Proceedings of the American Mathematical Society, vol. 17, pp. 352-357.
  • Aldweby, H., Darus, M., (2013), Univalence of a New General Integral Operator Associated with the q-Hypergeometric Function, International Journal of Mathematics and Mathematical Sciences, 2013, Article ID 769537, 5 pages.