참고문헌
- L.C. Andrews, Special functions for engineers and applied mathematicians, MacMillan, New York, USA, 1985.
- J. Choi, N.U. Khan, T. Usman and M. Aman, Certain unified polynomials, Integral Transforms and Special Functions 30(1) (2019), 1-13. https://doi.org/10.1080/10652469.2018.1511552
- J. Choi and P. Agarwal, Certain unified integrals involving a product of Bessel functions of first kind, Honam Mathematical J. 35 (4) (2013), 667-677. https://doi.org/10.5831/HMJ.2013.35.4.667
- J. Choi, P. Agarwal, S. Mathur and S.D. Purohit, Certain new integral formulas involving the generalized Bessel functions , Bull. Korean Math. Soc. 51 (4) (2014), 995-1003. https://doi.org/10.4134/BKMS.2014.51.4.995
- C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. London Math. Soc. 27 (1928), 389-400. https://doi.org/10.1112/plms/s2-27.1.389
- M. Kamarujjama, O. Khan, Computation of new class of integrals involving generalized Galue type Struve function, J. Comput. Appl. Math. 351 (2019), 228-236. https://doi.org/10.1016/j.cam.2018.11.014
- N.U. Khan, T. Usman and M.Ghayasuddin, A unified double integral associated with Whittaker functions, Journal of Nonlinear Systems and Applications, 5 (2016), 21-24.
- N.U. Khan, T. Usman and M. Ghayasuddin, Some integrals associated with multiindex Mittag-Leffler functions,J. Appl. Math. and Informatics, 34(3) (2016), 249-255. https://doi.org/10.14317/jami.2016.249
- N.U. Khan, M. Ghayasuddin, W. A. Khan and Sarvat Zia, On integral operator involving Mittag-Leffler function, J. Ramanujan Soc. Math. and Sci. 5(1) (2016), 147-154.
- 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.
- N.U. Khan, M.Ghayasuddin and T. Usman ,On certain integral formulas involving the product of Bessel function and Jacobi polynomial, Tamkang Journal of Mathematics, 47(3) (2016), 151-153.
- N.U. Khan, M.Ghayasuddin and S.Wali Khan, Some finite integrals involving the product of Bessel function with Jacobi and Laguerre polynomials, Commun. Korean Math. Soc. 33(3) (2018), 1013-1024. https://doi.org/10.4134/CKMS.C170237
- N.U. Khan, Raghib Nadeem, T. Usman and A.H. Khan, Evaluation of integral formulas associated with the product of generalized Bessel function with orhogonal polynomials, Homan Mathematical J. 41 (2019), 135-152.
- N.U. Khan, T. Usman and M. Aman, Generalized Wright function and its properties using extended beta function, Tamkang journal of Mathematics, 51(4) (2020), 349-363. https://doi.org/10.5556/j.tkjm.51.2020.3087
- N.U. Khan, T. Usman, M. Aman, S. Al-Omari and S. Araci, Computations of certain integral formulas involving generalized Wright function, Advances in Difference Equations, 2020:491
- N.U. Khan, T. Usman and M. Aman, Some properties concerning the analysis of generalized Wright function, Journal of Computational and Applied Mathematics, 376 (2020) 112840. https://doi.org/10.1016/j.cam.2020.112840
- N.U. Khan, M. Aman and T. Usman, Extended Beta, Hypergeometric and Confluent Hypergeometric functions, Transactions Issue Mathematics Series of physical- technical and mathematics science, Azerbaijan National Academy of Science, 39(1) 83-97.
- O. Khan, M. Kamarujjama and N.U. Khan, Certain integral transforms involving the Product of Galue type Stuve function and Jacobi Polynomial, Palestine Journal of Mathematics, 8(2) (2019), 191-199.
- V. Kiryakova, Some special functions related to fractional calculus and fractional (non integer) order control systems and equations, Facta Universitatis Series: Automatic Control and Robotics, 7 (1) (2008), 79-98.
- G. M. Mittag-Leffler, Sur la nouvellefonction Eα(x), Comptes Rendus de I'Academie des Sciences Paris, 137 (1903), 554-558.
- K.S. Nisar, D.L. Suthar, S.D. Purohit and H. Amsalu, Unified Integrals Involving Product of Multivariable Polynomials and Generalized Bessel Functions, Bol. Soc. Paran. Mat. (3s.) 38(6) (2020), 73-83.
- A.P. Prudnikov, Yu.A. Brychkov and O.I. Marichev, Integral and Series V.3.More special functions, New York-London: Gordon and Breach, (1992).
- I. Podlubny, Fractional differential equations, Academic Press, New York, USA, (1999).
- E.D. Rainville, Special functions, The Macmillan Company, New York (1960).
- M. El-Shahed and A. Salem, An extension of Wright function and its properties, J. Mathematics, 2015, (2015) Article ID 950728, 1-11.
- 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).
- H.M. Srivastava and J. Choi, Zeta and q-Zeta functions and associated series and integrals, Elsevier Science Publishers, Amsterdam, London and New York, (2012).
- H.M. Srivastava and M.C. Daoust, Certain generalized Neumann expansions associated with the kampe de Feriet function, Nederl. Akad. Wetensh. Proc. Ser. A Indag Math. 31 (1969), 449-457.
- H.M. Srivastava and M.C. Daoust, A note on the convergence of Kampe de Feriet's double hypergeometric series, Math.Nachr. 53 (1972), 151-159. https://doi.org/10.1002/mana.19720530114
- D.L. Suthar, H. Amsalu and K. Godifey, Certain integrals involving multivariate Mittag-Leffler function, Journal of Inequalities and Applications, (2019) 2019:208. https://doi.org/10.1186/s13660-019-2162-z
- D.L. Suthar, K. Tilahun and A. Oli, Generalized Fractional Calculus Operators Involving the Product of the Jacobi Type Orthogonal Polynomials and Multivariable Polynomials, Applications and Applied Mathematics, 15(1) (2020), 565-581.
- D.L. Suthar, S.D. Purohit, H. Habenom and J. Singh, Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function, Discrete and Continous Dynamical Systems Series S. (2021), doi: 10.3934/dcdss.2021019.
- H. Tadesse, D.L. Suthar, and M. Ayalew, Finite Integral Formulas Involving Multivariable Aleph-Functions, Journal of Applied Mathematics, 2019, Article ID 6821797, 10 pages.
- E.T. Whittaker and G.N. Watson, A course of modern analysis, 4th edition, Cambridge University Press, Cambridge London, New York, (1927).
- A. Wiman, Ber den Fundamentalsatz in der Theoric der Funktionen Eα(x), Acta Math. 29 (1905), 191-201. https://doi.org/10.1007/BF02403202