APPARENT INTEGRALS MOUNTED WITH THE BESSEL-STRUVE KERNEL FUNCTION

• Khan, N.U. (Department of Applied Mathematics, Aligarh Muslim University) ;
• Khan, S.W. (Department of Applied Mathematics, Aligarh Muslim University)
• Accepted : 2019.01.14
• Published : 2019.03.25
• 203 5

Abstract

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.

Keywords

Gamma function;generalized Hypergeometric function $_pF_q$;generalized (Wright) hypergeometric functions $_p{\Psi}_q$;Bessel-Struve kernel function $S_{\alpha}({\lambda}z)$;Macrobart integral formula and Edward integral formula;Fourier cosine transform;Fourier sine transform;Mellin transform

References

1. A.Erdelyi, W.Magnus, F.Oberhettinger and F.G.Tricomi, Tables of Integral Transforms, Vol-I, McGraw-Hill Book Company, New York, 1954.
2. A. Gasmi and M. Sifi, The Bessel-Struve interwining operator on C and mean periodic functions, IJMMS. 59 (2004), 3171-3185.
3. E.D.Rainville,Special functions, Macmillan, New York, 1960.
4. E.M.Wright,The asymptotic expansion of the generalized hypergeometric functions, J. London Math. Soc. 10 (1935), 286-293.
5. J.Edward, A treatise on the integral calculus, Vol.II, Chelsea Publishing Company, New York, 1922.
6. H.M.Srivastava and H.L.Manocha :A Treatise on generating functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and sons, New York, 1984.
7. J.Choi, P.Agarwal, S.Mathur and S.D.Purohit,Certain new integral formulas involving the generalized Bessel function, Bull.Korean Math. Soc. 51(4) (2014), 995-1003. https://doi.org/10.4134/BKMS.2014.51.4.995
8. MacRobert, T.M.Beta functions formulae and integrals involving E-function, Math. Annalen. 142 (1961), 450-452. https://doi.org/10.1007/BF01450936
9. N.U.Khan and M.Ghayasuddin, A new class of integral formulas associated with generalized Bessel function, Sohag J.Math. 3(2) (2016), 1-4. https://doi.org/10.18576/sjm/030101
10. N.U.Khan, M.Ghayasuddin, W.A.Khan and Sarvat Zia,Certain unified integral involving Generalized Bessel-Maitland function, South East Asian J. of Math and Math. Sci. 11(2) (2015), 27-36.
11. N.U.Khan, T.Usman and M.Ghayasuddin, Some integrals associated with multiindex Mittag-Leffler functions, J.Appl.Math. and Informatics. 34(3-4) (2016), 249-255. https://doi.org/10.14317/jami.2016.249
12. N.U.Khan, S.W.Khan and M.Ghayasuddin, Some new results associated with Bessel-Struve kernel function, Acta Universitatis Apulensis. 48 (2016), 89-101.
13. S.Jain, P.Agarwal, A new class of integral relations involving general class of polynomials and I-functions, Walialak J. Sci and tech. 12(11) (2015), 1009-1018.