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Summation Formulae for a Series Involving the I - Functions of Several Variables

Author(s):P C Sreenivas, T M Vidya, T M Vasudevan Nambisan, P V Maya

Affiliation: 1Principal, Gurudev Arts and Science College Mathil, Payyanur, 2Assistant Professor, Department of Mathematics, Mahatma Gandhi College Iritty, Kannur, Kerala, 3Emeritus Professor, College of Engineering Trikaripur, Kasargod, 4Assistant Professor, Department of Mathematics, Mahatma Gandhi College Iritty, Kannur, Kerala

Page No: 1-7

Volume issue & Publishing Year: Volume 2, Issue 6, June 2025

published on: 2025/06/30

Journal: International Journal of Advanced Multidisciplinary Application.(IJAMA)

ISSN NO: 3048-9350

DOI: https://doi.org/10.5281/zenodo.17523826

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Article Indexing:

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., & Saxena, R. K. (1976). Expansions of generalized H-functions. Indian Journal of Pure and Applied Mathematics, 7(3), 337–341.
  • 2) Dixon, A. C. (1903). Summation of a certain series. Proceedings of the London Mathematical Society, 35, 285–289.
  • 3) Mathai, A. M., & 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., & Shantha Kumari, K. (2014). A study of I-function of several complex variables. International Journal of Engineering Mathematics, 2014, Article ID 931395. https://doi.org/10.1155/2014/931395
  • 5) Rathie, A. K. (1997). A new generalization of generalized hypergeometric functions. Le Mathematiche, LII(II), 297–310.
  • 6) Shanthakumari, K., Vasudevan Nambisan, T. M., & Rathie, A. K. (2014). A study of the I-function of two variables. Le Mathematiche, LXIX(I), 285–305.
  • 7) Sharma, B. L. (1975). Sum of a double series. Proceedings of the American Mathematical Society, 52, 136–138.
  • 8) Sharma, B. L. (1976). A Watson’s theorem for double series. Journal of the London Mathematical Society, 13(2), 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., & Panda, R. (1976). Expansion theorem for the H-function of several complex variables. Journal für die Reine und Angewandte Mathematik, 28, 129–145.
  • 11) Nagar, V. (1994). A study of generalized hypergeometric series with applications. Ph.D. Thesis, Maharshi Dayanand Saraswati University, Ajmer, Rajasthan.