Abstract: Abstract- In this paper, we derive two new summation formulae for a class of series involving I – functions of several variables. These functions, which generalize many known special functions, play a crucial role in various branches of Mathematical analysis and applied Mathematics. By employing suitable techniques of summation and transformation, we establish compact and elegant expressions for these series under certain convergence conditions. These results contribute to the ongoing development of summation theorems for generalized special functions and may further applications in Mathematical analysis.
Keywords: I – function of several variables, Gamma function, Special functions, Pocchammer symbol

Reference :

1. Banerji, P.K and Saxena, R.K (1976). Expansions of Generalized H-functions. Indian J Pure and Appl. Math. 7, No.3, 337-341.
2. Dixon,A.C. Summation of a certain series, Proc:, London Math. Soc., 35 pp. 285-289, (1903)
3. Mathai, A.M and Saxena, R.K. (1978): The H-function with applications in Statistics and other disciplines, Wiley Eastern, New Delhi.
4. Prathima,J.,Vasudevan Nambisan, T.M and Shantha Kumari, K: A study of I-function of several Complex variables, International Journal of Engineering Mathematics, Volume 2014, Article ID 931395, http://dx.doi.org/10.1155/2014/931395 (January 2014).
5. Rathie, Arjun K. (1997), ‘A new generalization of generalized hypergeometric functions’, Le Mathematiche’, Vol.LII. Fas.II, 297-310.
6. Shanthakumari.K, Vasudevan Nambisan T.M, and Arjun K. Rathie (2014), ‘A study of the Ifunction of two variables’, LE MATHEMATICHE, Vol.LXIX (2014), Fasc. I, pp.285-305.
7. Sharma, B.L. (1975), Sum of a double series, Proc. Amer.Math.Soc.52, pp. 136-138
8. Sharma, B.L. (1976), A Watson’s theorem for double series, J.London.Math.Soc.(2) 13, pp. 95-96
9. Srivastava. H.M, Gupta. K.C, Goyal. S.P. (1982), The H-functions of one and two variables with applications, South Asian Publishers, New Delhi.
10.Srivastava, H.M. and R. Panda. (1976), ‘Expansion theorem for the H-function of several complex variables’, J. Reine Angew. Math.28,129-145.
11.Vishakha Nagar, ‘A study of Generalized hypergeometric series with applications’, approved by Maharshi Dayanand Saraswathi University, Ajmer (Rajasthan) 1994