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International Journal of Mathematics and Mathematical Sciences
Volume 2010, Article ID 309503, 26 pages
http://dx.doi.org/10.1155/2010/309503
Research Article

Extensions of Certain Classical Summation Theorems for the Series 2饾惞1, 3饾惞2, and 4饾惞3 with Applications in Ramanujan's Summations

1Department of Mathematics Education, Wonkwang University, Iksan 570-749, Republic of Korea
2Mathematics Department, College of Science, Suez Canal University, Ismailia 41522, Egypt
3Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, Muscat, Alkhod 123, Oman
4Vedant College of Engineering and Technology, Village-Tulsi, Post-Jakhmund, Bundi, Rajasthan State 323021, India

Received 20 May 2010; Revised 7 September 2010; Accepted 23 September 2010

Academic Editor: Teodor Bulboac膬

Copyright 漏 2010 Yong Sup Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [20 citations]

The following is the list of published articles that have cited the current article.

  • Junesang Choi, Arjun K. Rathie, and H. M. Srivastava, “ A generalization of a formula due to Kummer ,” Integral Transforms and Special Functions, vol. 22, no. 11, pp. 851–859, 2011. View at PublisherView at Google Scholar
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  • Yong Sup Kim, Junesang Choi, and Arjun K. Rathie, “Two Results For The Terminating F-3(2)(2) With Applications,” Bulletin of The Korean Mathematical Society, vol. 49, no. 3, pp. 621–633, 2012. View at PublisherView at Google Scholar
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  • Rathie, Paris, and Kim, “An extension of Saalschütz's summation theorem for the series r+3Fr+2,” Integral Transforms and Special Functions, vol. 24, no. 11, pp. 916–921, 2013. View at PublisherView at Google Scholar
  • Medhat A. Rakha, Mohamed M. Awad, and Arjun K. Rathie, “On an Extension of Kummer's Second Theorem,” Abstract and Applied Analysis, vol. 2013, pp. 1–6, 2013. View at PublisherView at Google Scholar
  • Arjun K. Rathie, and Adem Kiliçman, “On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial,” Advances in Difference Equations, vol. 2014, no. 1, 2014. View at PublisherView at Google Scholar
  • Junesang Choi, and Arjun Kumar Rathie, “New results for the series 2F1(x) with an application,” Communications of the Korean Mathematical Society, vol. 29, no. 1, pp. 65–74, 2014. View at PublisherView at Google Scholar
  • Junesang Choi, and Arjun K. Rathie, “Two general hypergeometric transformation formulas,” Communications of the Korean Mathematical Society, vol. 29, no. 4, pp. 519–526, 2014. View at PublisherView at Google Scholar
  • Yong S. Kim, Arjun. K. Rathie, and Richard B. Paris, “ An alternative proof of the extended Saalschütz summation theorem for the r + 3 F r + 2 (1) series with applications ,” Mathematical Methods in the Applied Sciences, 2015. View at PublisherView at Google Scholar
  • Junesang Choi, and Arjun K. Rathie, “Reducibility of the kampé de fériet function,” Applied Mathematical Sciences, vol. 9, no. 85-88, pp. 4219–4232, 2015. View at PublisherView at Google Scholar
  • Junesang Choi, and Arjun K. Rathie, “A summation formula for the series 3F2 due to fox and its generalizations,” Communications of the Korean Mathematical Society, vol. 30, no. 2, pp. 103–108, 2015. View at PublisherView at Google Scholar
  • Yong Sup Kim, Arjun Kumar Rathie, and Xiaoxia Wang, “π and other formulae implied by hypergeometric summation theorems,” Communications of the Korean Mathematical Society, vol. 30, no. 3, pp. 227–237, 2015. View at PublisherView at Google Scholar
  • Yongsup Kim, “New class of integrals involving generalized hypergeometric function and the logarithmic function,” Communications of the Korean Mathematical Society, vol. 31, no. 2, pp. 329–342, 2016. View at PublisherView at Google Scholar
  • Arjun K. Rathie, and Junesang Choi, “Reducibility of certain Kampé de Fériet function with an application to generating relations for products of two laguerre polynomials,” Filomat, vol. 30, no. 7, pp. 2059–2066, 2016. View at PublisherView at Google Scholar
  • Junesang Choi, Vivek Rohira, and Arjun K. Rathie, “Note on the extended watson’s summation theorem for the series 4F3(1),” Far East Journal of Mathematical Sciences, vol. 102, no. 11, pp. 2895–2902, 2017. View at PublisherView at Google Scholar
  • H. M. Srivastava, Yashoverdhan Vyas, and Kalpana Fatawat, “Extensions of the classical theorems for very well-poised hypergeometric functions,” Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017. View at PublisherView at Google Scholar
  • Mohammed M. Awad, Arjun K. Rathie, Asmaa O. Mohammed, and Medhat A. Rakha, “New series identities for 1 / π,” Communications of the Korean Mathematical Society, vol. 32, no. 4, pp. 865–874, 2017. View at PublisherView at Google Scholar
  • Young Sup Kim, Arjun Kumar Rathie, and Sebastien Gaboury, “Applications of extended Watson's summation theorem,” Turkish Journal of Mathematics, vol. 42, no. 2, pp. 418–443, 2018. View at PublisherView at Google Scholar