A general matrix series inversion pair and associated polynomials

References

[1] Askey, R.—Wilson, J.: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54(319) (1985), 1–55.10.1090/memo/0319Suche in Google Scholar

[2] Brafman, F.: Some generating functions for Laguerre and Hermite polynomials, Canad. J. Math. 9 (1957), 180–187.10.4153/CJM-1957-020-1Suche in Google Scholar

[3] Constantine, A. G.—Muirhead, R.: Partial differential equations for hypergeometric functions of two argument matrix, J. Multivariate Anal. 3 (1972), 332–338.10.1016/0047-259X(72)90020-6Suche in Google Scholar

[4] Dave, B. I.—Dalbhide, M.: Gessel-Stanton's inverse series and a system of q-polynomials, Bull. Sci. Math. 138 (2014), 323–334.10.1016/j.bulsci.2013.03.006Suche in Google Scholar

[5] Defez, E.—Hervás, A.—Law, A.—Villanueva-Oller, J.—Villanueva, R.: Progressive transmission of images: PC-based computations, using orthogonal matrix polynomials, Math. Comput. Modelling 32 (2000), 1125–1140.10.1016/S0895-7177(00)00195-3Suche in Google Scholar

[6] Defez, E.—Jódar, L.: Jacobi matrix differential equation, polynomial solutions, and their properties, Comput. Math. Appl. 48 (2004), 789–803.10.1016/j.camwa.2004.01.011Suche in Google Scholar

[7] Dunford, N.—Schwartz, J.: Linear Operators, part I, General theory, vol. I., Interscience Publishers, INC., New York, 1957.Suche in Google Scholar

[8] Gould, H. W.: Some generalizations of Vandermonde's convolution, Amer. Math. Monthly 63(2) (1956), 84–91.10.1080/00029890.1956.11988763Suche in Google Scholar

[9] Gould, H. W.: A new convolution formula and some new orthogonal relations for inversion of series, Duke Math. J. 29(3) (1962), 393–404.10.1215/S0012-7094-62-02938-1Suche in Google Scholar

[10] Gould, H. W.: A new series transform with applications to Bessel, Legendre, and Tchebycheff polynomials, Duke Math. J. 31(2) (1964), 325–334.10.1215/S0012-7094-64-03131-XSuche in Google Scholar

[11] Gould, H. W.: Inverse series relations and other expansions involving Humbert polynomials, Duke Math. J. 32(4) (1965), 697–711.10.1215/S0012-7094-65-03275-8Suche in Google Scholar

[12] Gould, H. W.—Hsu, L. C.: Some new inverse series relations, Duke Math. J. 40(4) (1973), 885–891.10.1215/S0012-7094-73-04082-9Suche in Google Scholar

[13] Hille, H.: Lectures on Ordinary Differential Equations, Addison-Wesley, New York, 1969.Suche in Google Scholar

[14] James, A. T.: Special Functions of Matrix and Single Argument in Statistics. In: Theory and Applications of Special Functions, Academic Press, New York, 1975.10.1016/B978-0-12-064850-4.50016-1Suche in Google Scholar

[15] Jódar, L.—Company, R.—Navarro, E.: Laguerre matrix polynomials and systems of second-order differential equations, Appl. Numer. Math. 15 (1994), 53–63.10.1016/0168-9274(94)00012-3Suche in Google Scholar

[16] Jódar, L.—Company, R.—Ponsoda, E.: Orthogonal matrix polynomials and systems of second order differential equations, Diff. Equations and Dynamic Syst. 3(3) (1995), 269–228.Suche in Google Scholar

[17] Jódar, L.—Cortés, J. C.: On the hypergeometric matrix function, J. Comput. Appl. Math. 99 (1998), 205–217.10.1016/S0377-0427(98)00158-7Suche in Google Scholar

[18] Jódar, L.—Defez, E.—Ponsoda, E.: Matrix quadrature integration and orthogonal matrix polynomials, Congr. Numer. 106 (1995), 141–153.Suche in Google Scholar

[19] Jódar, L.—Cortés, J. C.: Some properties of Gamma and Beta matrix functions, Appl. Math. Lett. 11(1) (1998), 89–93.10.1016/S0893-9659(97)00139-0Suche in Google Scholar

[20] Khatri, C. G.: Partial differential equations for hypergeometric functions of two argument matrices, J. Multivariate Anal. 12(2) (1972), 201–207.10.1016/0047-259X(72)90027-9Suche in Google Scholar

[21] Koelink E.—Walter Van Assche (Eds.): Orthogonal Polynomials and Special Functions, Springer, 2003.10.1007/b12166Suche in Google Scholar

[22] Panda, R.: On a new clas of polynomials, Glasgow Math. J. 18 (1977), 105–108.10.1017/S0017089500003116Suche in Google Scholar

[23] Pathan, M.—Bin-Saad Maged, G.—Al-Sarahi, F.: On mathrix polynomial associated with Humbert polynomial, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math. 21(3) (2014), 207–218.10.7468/jksmeb.2014.21.3.207Suche in Google Scholar

[24] Rainville, E. D.: Special Functions, Mac Millan Co., New York, 1960.Suche in Google Scholar

[25] Riordan, J.: An Introduction to Combinatorial Identities, Wiley, New York – London – Sydney, 1968.Suche in Google Scholar

[26] Sanjhira, R.—Dave, B.I.: Generalized Konhauser matrix polynomial and its properties, Math. Student 87(3–4) (2018), 109–120.Suche in Google Scholar

[27] Sanjhira, R.—Nathwani, B. V.—Dave, B. I.: Generalized Mittag-Leffler matrix function and associated matrix polynomials, J. Indian Math. Soc. 86(1–2) (2019), 161–178.Suche in Google Scholar

[28] Sanjhira, R.: A general inverse matrix series relation and associated polynomials – II, Math. Slovaca 71(2) (2021), 301–316.10.1515/ms-2017-0469Suche in Google Scholar

[29] Shehata, A.: A new kind of Legendre matrix polynomials, Gazi University Journal of Science 29(2) (2016), 435–457.Suche in Google Scholar

[30] Shehata, A.: Some relation on Konhauser matrix polynomial, Miskolc Math. Notes 17(1) (2016), 605–633.10.18514/MMN.2016.1126Suche in Google Scholar

[31] Srivastava, H. M.: The Weyl fractional integral of general class of polynomials, Boll. Un. Mat. Ital. 6(2B) (1983), 219–228.Suche in Google Scholar