On Some Definite Integrals from Ramanujan's Notebooks

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Authors

  • Ramesh Kumar Muthumalai
     Department of Mathematics, Saveetha Engineering College, Saveetha Nagar, Thandalam, Chennai - 602 105 ,IN

Keywords:

Definite Integrals, Special Functions, Infinite Series, Infinite Products, Ramanujan's Notebooks.
Calculus

Abstract

Some definite integrals involving powers of inverse trigonometric functions that are found in the chapter 9 of Ramanujan notebooks (Part-I) are evaluated through elementary methods. Further, we present some identities connecting integrals with some infinite series and infinite products.

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Published

2015-12-01

How to Cite

Muthumalai, R. K. (2015). On Some Definite Integrals from Ramanujan’s Notebooks. The Journal of the Indian Mathematical Society, 82(3-4), 115–126. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/1687

Issue

Volume 82, Issue 3-4, July-December 2015

Section

Articles

License

Copyright (c) 2015 Ramesh Kumar Muthumalai

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

A. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formula & graphs, and mathematical tables, Dover publications, Inc., Newyork, 1965.

B. C. Berndt, Ramanujan's notebooks, Part-V, Springer-Verlag, USA, 1998.

B. C. Berndt, Ramanujan's notebooks, Part-I, Springer-Verlag, USA, 1985.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, 6 Ed, Academic Press, USA, 2000.

K. S. Miller and B. Ross, An Introduction To The Fractional Calculus And Fractional Differential Equations, John Wiley & Sons, USA, 1993.

S. Ramanujan, On the integral R xtan−1t t dt, J. Indian Math. Soc., VII (1915), 93–96.