On the hyper-gamma function

Year 2017, Volume: 5 Issue: 1, 64 - 69, 30.04.2017

Mustafa Bahşi Süleyman Solak

https://doi.org/10.36753/mathenot.421700

Abstract

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.

Keywords

Gamma function, generalization, hyper-gamma function

References

• [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.