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ANOTHER METHOD FOR A KUMMER-TYPE TRANSFORMATION FOR A 2F2 HYPERGEOMETRIC FUNCTION

  • Choi, June-Sang (DEPARTMENT OF MATHEMATICS DONGGUK UNIVERSITY) ;
  • Rathie, Arjun K. (DEPARTMENT OF MATHEMATICS GOVT. P. G. COLLEGE)
  • Published : 2007.07.31

Abstract

Very recently, by employing an addition theorem for the con-fluent hypergeometric function, Paris has obtained a Kummer-type trans-formation for a $_2F_2(x)$ hypergeometric function with general parameters in the form of a sum of $_2F_2(-x)$ functions. The aim of this note is to derive his result without using the addition theorem.

Keywords

generalized hypergeometric function;Kummer's first theorem for $_1F_1$;Kummer-type transformation;addition theorem for $_1F_1$

References

  1. R. B. Paris, A Kummer-type transformation for $\alpha_{2}F_{2}$ hypergeometric function, J. Comput. Appl. Math. 173 (2005), 379-382 https://doi.org/10.1016/j.cam.2004.05.005
  2. L. J. Slater, Confluent Hypergeometric Functions, Cambridge University Press, Cambridge, 1960
  3. L. J. Slater, neralized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966