Generalizations and applications of Srinivasa Ramanujan’s integral associated with infinite Fourier sine transforms in terms of Meijer’s G-function

References

[1] W. N. Bailey, Generalized Hypergeometric Series, Cambridge Tracts in Math. Math. Phys. 32, Cambridge University, Cambridge, 1935. Search in Google Scholar

[2] B. C. Berndt, Integrals associated with Ramanujan and elliptic functions, Ramanujan J. 41 (2016), no. 1–3, 369–389. 10.1007/s11139-016-9793-1Search in Google Scholar

[3] B. C. Berndt and A. Straub, Certain integrals arising from Ramanujan’s notebooks, SIGMA Symmetry Integrability Geom. Methods Appl. 11 (2015), Paper No. 083. 10.3842/SIGMA.2015.083Search in Google Scholar

[4] S. A. Dar and R. B. Paris, On integrals involving quotients of hyperbolic functions, J. Ramanujan Math. Soc. 36 (2021), no. 1, 23–32. Search in Google Scholar

[5] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions. Vol. 1, McGraw-Hill, New York, 1953. Search in Google Scholar

[6] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms. Vol. 1, McGraw-Hill, New York, 1954. Search in Google Scholar

[7] A. A. Kilbas and M. Saigo, H-Transforms: Theory and Applications (Analytical Methods and Special Functions). Vol. 9, Chapman & Hall/CRC, Boca Raton, 2004. 10.1201/9780203487372Search in Google Scholar

[8] A. A. Kilbas, M. Saigo and J. J. Trujillo, On the generalized Wright function, Fract. Calc. Appl. Anal. 5 (2002), no. 4, 437–460. Search in Google Scholar

[9] J. L. Meyer, A generalization of an integral of Ramanujan, Ramanujan J. 14 (2007), no. 1, 79–88. 10.1007/s11139-006-9004-6Search in Google Scholar

[10] F. Oberhettinger, Tables of Fourier Transforms and Fourier Transforms of Distributions, Springer, Berlin, 1990. 10.1007/978-3-642-74349-8Search in Google Scholar

[11] M. I. Qureshi and S. A. Dar, Evaluation of some definite integrals of Ramanujan, using hypergeometric approach, Palest. J. Math. 7 (2018), no. 2, 620–623. Search in Google Scholar

[12] M. I. Qureshi and S. A. Dar, Generalizations of Ramanujan’s integral associated with infinite Fourier cosine transforms in terms of hypergeometric functions and its applications, Kyungpook Math. J. 60 (2020), no. 4, 781–795. Search in Google Scholar

[13] M. I. Qureshi and S. A. Dar, Some Hypergeometric Summation Theorems and Reduction Formulas via Laplace Transform Method, Montes Taurus J. Pure Appl. Math. 3 (2021), no. 3, 182–199. Search in Google Scholar

[14] M. I. Qureshi and I. H. Khan, Ramanujan integrals and other definite integrals associated with Gaussian hypergeometric functions, South East Asian J. Math. Math. Sci. 4 (2005), no. 1, 39–52. Search in Google Scholar

[15] M. I. Qureshi, K. A. Quraishi and R. Pal, A class of hypergeometric generalizations of an integral of Srinivasa Ramanujan, Asian J. Current Eng. Math. 2 (2013), no. 3, 190–194. Search in Google Scholar

[16] M. I. Qureshi, K. A. Quraishi and R. Pal, Some applications of celebrated master theorem of Ramanujan, British J. Math. Comp. Sci. 4 (2014), no. 20, 2862–2871. 10.9734/BJMCS/2014/4842Search in Google Scholar

[17] E. D. Rainville, Special Functions, The Macmillan, New York, 1971. Search in Google Scholar

[18] S. Ramanujan, Some definite integrals, J. Indian Math. Soc. 11 (1915), 81–87. Search in Google Scholar

[19] S. Ramanujan, Some definite integrals connected with Gauss’s sums, Mess. Math. 44 (1915), 75–86. Search in Google Scholar

[20] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood, New York, 1984. Search in Google Scholar

[21] H. M. Srivastava, M. I. Qureshi and S. A. Dar, Some novel Laplace-transform based integrals via hypergeometric techniques, Appl. Math. Inf. Sci. 14 (2020), no. 5, 743–754. 10.18576/amis/140501Search in Google Scholar

[22] H. M. Srivastava, M. I. Qureshi, R. Singh and A. Arora, A family of hypergeometric integrals associated with Ramanujan’s integral formula, Adv. Stud. Contemp. Math. (Kyungshang) 18 (2009), no. 2, 113–125. Search in Google Scholar

[23] E. M. Wright, The asymptotic expansion of thegeneralized Bessel function, Proc. Lond. Math. Soc. (2) 38 (1935), 257–270. 10.1112/plms/s2-38.1.257Search in Google Scholar

[24] E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. Lond. Math. Soc. (2) 46 (1940), 389–408. 10.1112/plms/s2-46.1.389Search in Google Scholar