On the hyper-gamma function

In this paper, we introduce a new generalization for the gamma function as hyper-gamma function. Some identities and integral representation are obtained for the this new generalization.

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  • [1] Alzer, H., Inequalities for Euler’s gamma function, Forum Math., 20(6)(2008), 955–1004.
  • [2] Anderson, G.D. and Qiu, S.-L., A monotonicity property of the gamma function, Proc. Amer. Math. Soc., 125(1997), 3355–3362.
  • [3] Anderson, G.D., Vamanamurthy, M. K. and Vuorinen, M., Special functions of quasiconformal theory, Exposition. Math., 7(1989), 97-136.
  • [4] Batir, N., Inequalities for the gamma function, Arch. Math., 91(2008), 554–563.
  • [5] Chaudhry, M.A. and Zubair, S.M., Generalized incomplete gamma functions with applications, J. Comput. Appl. Math., 55(1994), 99–124.
  • [6] Chaudhry, M.A., Qadir, A., Rafique, M. and Zubair, S.M., Extension of Euler’s beta function, J. Comput. Appl. Math., 78(1997), 19–32.
  • [7] Chaudhry, M.A. and Zubair, S.M., On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms, J. Comput. Appl. Math., 59(1995), 253–284.
  • [8] Chaudhry, M.A. and Zubair, S.M., Extended incomplete gamma functions with applications, J. Math. Anal. Appl., 274(2002), 725–745.
  • [9] Conway, J.H. and Guy, R.K., The book of numbers, Springer-Verlag, New York, 1996.
  • [10] Dil, A. and Mezö, I., A symmetric algorithm hyperharmonic and Fibonacci numbers, Appl. Math. Comput., 206(2008), 942–951.
  • [11] Graham, R.L., Knuth, D.E. and Patashnik, O., Concrete mathematics, Addison Wesley, 1993.
  • [12] Whittaker, E.T. and Watson, G.N., A Course of Modern Analysis, Cambridge Univ. Press, Cambridge, 1958.