Certain integral transforms concerning the product of family of polynomials and generalized incomplete functions

Meena, Sapna; Bhatter, Sanjay; Jangid, Kamlesh; Purohit, Sunil Dutt

doi:10.2478/mjpaa-2020-0019

Abstract

In this article, we have derived some integral transforms of the polynomial weighted incomplete H-functions and incomplete ̄H-functions. The obtained image formulas are of general nature and may, as special cases, give rise to integral transforms involved with the H-functions and ̄H-functions.

References

[1] S.K.Q. Al-Omari, D. Baleanu and S.D. Purohit, Some results for Laplace-type integral operator in quantum calculus, Adv. Difference Equ., 2018 (2018), 124.10.1186/s13662-018-1567-1
Search in Google Scholar Back to article
[2] A. Baricz, Generalized Bessel Functions of the First Kind, Lecture Notes in Mathematics, Vol. 1994, Springer, Berlin, Germany (2010).10.1007/978-3-642-12230-9
Search in Google Scholar Back to article
[3] R.G. Buschman and H.M. Srivastava, The H-function associated with certain class of Feynman integral, J. Phys. A: Math. Gen., 23 (1990), 4707-4710.10.1088/0305-4470/23/20/030
Search in Google Scholar Back to article
[4] J. Choi, R.K. Parmar and P. Chopra, The incomplete Srivastavas triple hypergeometric functions γHB and ΓHB, Filomat, 30 (2016), 17791787.10.2298/FIL1607779C
Search in Google Scholar Back to article
[5] A. Erdélyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi, Higher Transcendental Functions, McGraw-Hill Book Company, New York, Toronto and London, Vols. I and II (1954).
Search in Google Scholar Back to article
[6] A. Erdélyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi, Tables of Integral Transforms, McGraw-Hill Book Company, New York, Toronto and London, Vols. I and II (1954).
Search in Google Scholar Back to article
[7] H. Exton, Multiple Hypergeometric Functions and Applications, Ellis Horwood, Chichester, UK (1976).
Search in Google Scholar Back to article
[8] A.A. Inayat-Hussain, New properties of hypergeometric series derivable from Feynman integrals. II: A generalisations of the H-function, J.Phys. A, 20 (1987), 4119-4128.10.1088/0305-4470/20/13/020
Search in Google Scholar Back to article
[9] K. Jangid, S. Bhatter, S. Meena, D. Baleanu, M.A. Qurashi and S.D. Purohit, Some fractional calculus findings associated with the incomplete I-functions, Adv. Differ. Equ., 2020 (2020): 265.10.1186/s13662-020-02725-7
Search in Google Scholar Back to article
[10] A.A. Kilbas and M. Saigo, H-Transforms: Theory and Applications, 9, CRC Press, London and New York (2004).
Search in Google Scholar Back to article
[11] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, 204, Elsevier (North-Holland) Science Publishers, Amsterdam, London and New York (2006).
Search in Google Scholar Back to article
[12] A.M. Mathai and R.K. Saxena, The H-Function with Applications in Statistics and Other Disciplines, Wiley Eastern Limited New Delhi; John Wiley and Sons, New York (1978).
Search in Google Scholar Back to article
[13] A.M. Mathai, R.K. Saxena and H.J. Haubold, The H-Functions: Theory and Applications Springer, New York (2010).
Search in Google Scholar Back to article
[14] A.C. McBride, Fractional Calculus and Integral Transforms of Generalized Functions, Research Notes in Mathematics, Vol. 31, Pitman, London, UK (1979).
Search in Google Scholar Back to article
[15] S. Meena, S. Bhatter, K. Jangid, and S.D. Purohit, Certain expansion formulae of incomplete H-functions associated with Leibniz rule, TWMS J. App. Eng. Math., (2020), Accepted.10.48185/jfcns.v2i1.231
Search in Google Scholar Back to article
[16] R.K. Parmar and R.K. Saxena, The incomplete generalized τ-hypergeometric and second τ-Appell functions, J. Korean Math. Soc., 53 (2016), 363-379.10.4134/JKMS.2016.53.2.363
Search in Google Scholar Back to article
[17] R.K. Parmar and R.K. Saxena, Incomplete extended Hurwitz-Lerch Zeta functions and associated properties, Commun. Korean Math. Soc., 32 (2017), 287-304.10.4134/CKMS.c150227
Search in Google Scholar Back to article
[18] S.D. Purohit, Solutions of fractional partial differential equations of quantum mechanics, Adva. Appl. Math. Mech., 5(5) (2013), 639-651.10.4208/aamm.12-m1298
Search in Google Scholar Back to article
[19] S.D. Purohit, A.M. Khan, D.L. Suthar and S. Dave, The impact on raise of environmental pollution and occurrence in biological populations pertaining to incomplete H-function, Natl. Acad. Sci. Lett., (2020). doi.org/10.1007/s40009-020-00996-y10.1007/s40009-020-00996-y
Search in Google Scholar Back to article
[20] I.N. Sneddon, The Use of Integral Transforms, Tata McGraw-Hill, New Delhi (1979).
Search in Google Scholar Back to article
[21] H. M. Srivastava, Certain properties of a generalized Whittaker transform, Math. Cluj, 10 (33) (1968), 385–390.
Search in Google Scholar Back to article
[22] H. M. Srivastava, M.A. Chaudhry and R.P. Agarwal, The incomplete Pochhammer symbols and their applications to hypergeometric and related functions, Integral Transforms Spec. Funct., 23 (2012), 659–683.10.1080/10652469.2011.623350
Search in Google Scholar Back to article
[23] H.M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science, Amsterdam, The Netherlands (2012).10.1016/B978-0-12-385218-2.00002-5
Search in Google Scholar Back to article
[24] H.M. Srivastava, R.K. Saxena and R.K. Parmar, Some families of the incomplete H-functions and the incomplete ̄H-functions and associated integral transforms and operators of fractional calculus with applications, Russian J. Math. Phys., 25 (2018), 116-138.10.1134/S1061920818010119
Search in Google Scholar Back to article
[25] R. Srivastava, R. Agarwal and S. Jain, A family of the incomplete hypergeometric functions and associated integral transform and fractional derivative formulas, Filomat, 31 (2017), 125-140.10.2298/FIL1701125S
Search in Google Scholar Back to article
[26] R. Srivastava and N.E. Cho, Generating functions for a certain class of incomplete hypergeometric polynomials, Appl. Math. Comput., 219 (2012), 3219-3225.10.1016/j.amc.2012.09.059
Search in Google Scholar Back to article
[27] D.L. Suthar, S.D. Purohit and K.S. Nisar, Integral transforms of the Galue type Struve function, TWMS J. Appl. & Eng. Math., 8(1) (2018), 114–121.
Search in Google Scholar Back to article
[28] D.L. Suthar, A.M. Khan, A. Alaria, S.D. Purohit, J. Singh, Extended Bessel-Maitland function and its properties pertaining to integral transforms and fractional calculus, AIMS Mathematics, 5(2) (2020), 1400–1410.10.3934/math.2020096
Search in Google Scholar Back to article
[29] H.M. Srivastava, A contour integral involving Fox’s H-function, Indian J. Math., 14 (1972), 1–6.
Search in Google Scholar Back to article

Certain integral transforms concerning the product of family of polynomials and generalized incomplete functions

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