An interesting integral involving product of two generalized hypergeometric function
DOI:
https://doi.org/10.5269/bspm.51949Abstract
In this research note, an interesting integral involving hypergeometric function has been evaluated in terms of gamma function. It is further used to evaluate an integral involving product of two generalized hypergeometric functions. A few very interesting special cases have also been given
References
1. Andrews, G. E., Askey, R. and Roy, R., Special functions, Encyclopaedia of Mathematics and it's applications, Cambridge University Press, Cambridge, (1989).
2. Bailey, W. N., Products of generalized hypergeometric series, Proc. London Math. Soc., 28(2), 242-254, (1928). https://doi.org/10.1112/plms/s2-28.1.242
3. Bailey, W. N., Generalized Hypergeometric Series, Cambridge University Press, Cambridge, (1935), reprinted by stechert Hafner, New York, (1964).
4. Brychkov, Yu. A., Evaluation of some classes of definite and indefinite integrals, Integral Transforms Spec. Funct., 13, 163-167,(2002). https://doi.org/10.1080/10652460212896
5. Kim, Y. S., Rakha, M. A., and Rathie, A. K., Extensions of certain of classical summations theorems for the series 2F1, 3F2 and 4F3 with applications in Ramanujan's summations, Int. J. Math. Math. Sci., Volume 2010, Article ID 309503, 26 pages,(2010). https://doi.org/10.1155/2010/309503
6. MacRobert, T. M., Beta function formulae and integrals involving E-function, Math. Annalen, 52, 451-452, (1960-1961). https://doi.org/10.1007/BF01450936
7. Prudnikov, A.P., Brychkov, Yu. A., and Marichev, O.I., Integrals and series. Volume 3: More Special Functions, Gordon and Breach Sci. Pul., New York, (1990).
8. Rainville, E. D., Special Functions, The Macmillan Company, New York, (1960); reprinted by Chelsea Publishing Company, Bronx, New York,
2. Bailey, W. N., Products of generalized hypergeometric series, Proc. London Math. Soc., 28(2), 242-254, (1928). https://doi.org/10.1112/plms/s2-28.1.242
3. Bailey, W. N., Generalized Hypergeometric Series, Cambridge University Press, Cambridge, (1935), reprinted by stechert Hafner, New York, (1964).
4. Brychkov, Yu. A., Evaluation of some classes of definite and indefinite integrals, Integral Transforms Spec. Funct., 13, 163-167,(2002). https://doi.org/10.1080/10652460212896
5. Kim, Y. S., Rakha, M. A., and Rathie, A. K., Extensions of certain of classical summations theorems for the series 2F1, 3F2 and 4F3 with applications in Ramanujan's summations, Int. J. Math. Math. Sci., Volume 2010, Article ID 309503, 26 pages,(2010). https://doi.org/10.1155/2010/309503
6. MacRobert, T. M., Beta function formulae and integrals involving E-function, Math. Annalen, 52, 451-452, (1960-1961). https://doi.org/10.1007/BF01450936
7. Prudnikov, A.P., Brychkov, Yu. A., and Marichev, O.I., Integrals and series. Volume 3: More Special Functions, Gordon and Breach Sci. Pul., New York, (1990).
8. Rainville, E. D., Special Functions, The Macmillan Company, New York, (1960); reprinted by Chelsea Publishing Company, Bronx, New York,
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2022-02-06
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