Volume 67 | Issue 8 | Year 2021 | Article Id. IJMTT-V67I8P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I8P510
Dr. R. Sivaraman, "Ramanujan Summation for Classic Combinatorial Problem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 8, pp. 82-87, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I8P510
The concept of Ramanujan Summation has been dealt with several forms in recent decades. In this paper, I will define Ramanujan summation evaluated through a definite integral and using this, I had computed the Ramanujan summation for the divergent series whose terms represent the maximum number of regions formed by considering n points in the circumference of a circle which are joined by chords. This classic geometric problem along with Ramanujan summation method has produced an interesting and new result which is derived in detail in this paper.
[1] R. Sivaraman, Understanding Ramanujan Summation, International Journal of Advanced Science and Technology, 29(7) (2020) 1472 – 1485.
[2] R. Sivaraman,Sum of powers of natural numbers, AUT AUT Research Journal, 11(4) (2020) 353 – 359.
[3] S. Ramanujan, Manuscript Book 1 of Srinvasa Ramanujan, First Notebook, Chapter VIII, 66 – 68.
[4] Bruce C. Berndt, Ramanujan’s Notebooks Part II, Springer, Corrected Second Edition, (1999).
[5] G.H. Hardy, J.E. Littlewood, Contributions to the theory of Riemann zeta-function and the theory of distribution of primes, Acta Arithmetica, 41(1) (1916) 119 – 196.
[6] S. Plouffe , Identities inspired by Ramanujan Notebooks II , part 1, July 21 (1998), and part 2, April (2006).
[7] Bruce C. Berndt, An Unpublished Manuscript of Ramanujan on Infinite Series Identities, Illinois University, American Mathematical Society publication
[8] R. Sivaraman, Remembering Ramanujan, Advances in Mathematics: Scientific Journal, 9(1) (2020) 489–506.
[9] R. Sivaraman, Bernoulli Polynomials and Ramanujan Summation, Proceedings of First International Conference on Mathematical Modeling and Computational Science, Advances in Intelligent Systems and Computing, 1292 (2021) 475 – 484.
[10] B. Candelpergher, H. Gopalakrishna Gadiyar, R. Padma, Ramanujan Summation and the Exponential Generating Function, Cornell University, (2009).