المؤلفون: 呂漢軍, Lu, Han-Chun

المساهمون: 淡江大學數學學系博士班, 錢傳仁

مصطلحات موضوعية: 超幾何函數與超幾何多項式, Srivastava多項式, Bedient多項式和廣義Bedient多項式, Cesaro多項式和廣義Cesaro多項式, Shively’s pseudo-Laguerre多項式, 拉格朗日多項式, 雅可比多項式, 拉蓋爾多項式, 貝索多項式和廣義貝索多項式, 赫爾米特多項式, 多重積分表示式, Gamma函數, Eulerian beta積分公式, 線性化關係, Pochhammer符號, Hypergeometric functions and hypergeometric polynomials, Srivastava polynomials, Bedient polynomials and the generalized Bedient polynomials of the first and second kinds, Cesaro polynomials and the generalized Cesaro polynomials, Lagrange polynomials, Shively’s pseudo-Laguerre polynomials, Bessel polynomials and the generalized Bessel polynomials, Jacobi polynomials, Laguerre polynomials, Hermite polynomials, Multiple integral representations, Gamma function, Eulerian beta integral, Linearization relationship, Pochhammer symbol

العلاقة: References [1] W. A. Al-Salam, The Bessel polynomials, Duke Math. J. 24 (1957), 529–545. [2] A. Altın, E. Erku¸s and M. A. ¨ Ozarslan, Families of linear generating functions for polynomials in two variables, Integral Transforms Spec. Funct. 17 (2006), 315 320. [3] P. Appell and J. Kamp´e de F´eriet, Fonctions hyp´ergeom´etriques et hyperspheriques, Polynˆomes d’Hermite Gauthier-Villars, Paris, 1926. [4] W. N. Bailey, An integral representation for the product of two Hermite polynomials, J. London Math. Soc. (1938) s1-13 (3), 202-203. [5] L. Carlitz, An integral for the product of two Laguerre polynomials, Boll. Un.Mat. Ital. (3) 17 (1962) 25–28. [6] W.-C. C. Chan, C.-J. Chyan and H. M. Srivastava, The lagrange polynomials in several variables, Integral Transform. Spec. Funct., 12 (2001), 139–148. [7] S. K. Chatterjea, An integral representation for the product of two generalized Bessel polynomials, Boll. Un. Mat. Ital. (3) 18 (1963) 377–381. [8] S. K. Chatterjea, Integral representation for the product of two Jacobi polynomials, J. London Math. Soc. 39 (1964) 753-756. [9] S. K. Chatterjea, Some generating functions, Duke Math. J. 32 (1965), 563–564. [10] K.-Y. Chen, S.-J. Liu and H. M. Srivastava, Some new results for the Lagrange polynomials in several variables. ANZIAM J., 49 (2007), 243–258. [11] A. Erd´elyi, W. Magnus, F. Oberhettinger and F. G.Tricomi, Higher Transcendental Functions, Vol. I, McGraw Hill Book Company, New York, Toronto and London, 1953. [12] A. Erd´elyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vol. III, McGraw Hill Book Company, New York, Toronto and London, 1955. [13] E. Erku¸s and H. M. Srivastava, A unified presentation of some families of multivariable polynomials, Integral Transforms Spec. Funct. 17 (2006), 267–273. [14] E. Erku¸s, O. Duman and H. M. Srivastava, Statistical approximation of certain positive linear operators by means of the Chan-Chyan-Srivastava polynomials, Appl. Math. Comput. 182 (2006), 213–222. [15] H. Exton, Multiple Hypergeometric Functions and Applicaions. John Wiley and Sons (Halsted Press), New York; Ellis Horwood, Chichester (1976). [16] B. Gonz´alez, J. Matera and H. M. Srivastava, Some q generating functions and associated generalized hypergeometric polynomials, Math. Comput. Modelling 34 (1/2) (2001), 133–175. [17] E. Grosswald, Bessel Polynomials, Lecture Notes in Mathematics, Vol. 698, Springer-Verlag, Berlin, Heidelberg and New York, 1978. [18] W. T. Howell, Integral representations for products of Weber’s parabolic cylinder functions, Phil. May. (7), 25 (1938), 456–458. [19] M. A. Khan, A. K. Shukla, On Lagrange’s polynomials of three variables. Proyecciones 17 (1998), 227–235. [20] H. L. Krall and O. Frink, A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100–115. [21] G. Lauricella, Sulle funzioni ipergeometriche a pi´u variabili, Rend. Circ. Mat. Palermo, 7 (1893), 111–158. [22] S.-D. Lin, Y.-S. Chao and H. M. Srivastava, Some families of hypergeometric polynomials and associated integral representations, J. Math. Anal. Appl. 294 (2004), 399–411. [23] S.-D. Lin, S.-J. Liu and H. M. Srivastava, Some families of hypergeometric polynomials and associated multiple integral representations, Integral Transforms Spec. Funct. 22 (2011), 403–414. [24] S.-D. Lin, H. M. Srivastava and P.-Y. Wang, Some families of hypergeometric transformations and generating relations, Math. Comput. Modelling 36 (2002), 445–459. [25] S.-D. Lin, S.-J. Liu, H.-C. Lu and H. M. Srivastava, Integral representations for the generalized Bedient polynomials and the generalized Ces`aro polynomials, 218 (2011), 1330–1341. [26] S.-D. Lin, H. M. Srivastava and P.-Y. Wang, Some mixed multilateral generating relations involving hypergeometric functions, Integral Transforms Spec. Funct. 16 (2005), 609–614. [27] S.-D. Lin, S.-T. Tu and H. M. Srivastava, Some generating functions involving the Stirling numbers of the second kind, Rend. Sem. Mat. Univ. Politec. Torino 59 (2001), 199–224. [28] S.-J. Liu, C.-J. Chyan, H.-C. Lu and H. M. Srivastava, Multiple integral representations for some families of hypergeometric and other polynomials, Math. Comput. Modelling 54 (2011), 1420–1427. [29] S.-J. Liu, Bilateral generating functions for the Lagrange polynomials and the Lauricella functions, Integral Transforms Spec. Funct., 20 (7) (2009), 519–527. [30] W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Die Grundlehren der Mathematischen Wissenschften in Einzeldarstellungen mit Besonderer Ber¨ucksichtigung der Anwendungsgebiete, Band 52, Third enlarged edition, Springer-Verlag, Berlin, New York and Heidelberg, 1966. [31] H. L. Manocha, An integral representation for the product of two generalized Rice’s polynomials, Collect. Math. 20 (1969), 270–276. [32] E. ¨ Ozergin, M. A. ¨ Ozarslan and H. M. Srivastava, Some families of generating functions for a class of bivariate polynomials, Math. Comput. Modelling 50 (2009), 1113–1120. [33] M. I. Qureshi, M. Sadiq Khan and M. A. Pathan, Some multiple Gaussian hypergeometric generalizations of Buschman-Srivastava theorem. Int. J. Math. Math. Sci., (2005), 143–153. [34] E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971. [35] H. M. Srivastava, A contour integral involving Fox’s H-function, Indian J. Math. 14 (1972), 1–6. [36] H. M. Srivastava, Some orthogonal polynomials representing the energy spectral functions for a family of isotropic turbulence fields, Zeitschr. Angew. Math. Mech. 64 (1984), 255–257. [37] H. M. Srivastava, Some integral representations for the Jacobi and related hypergeometric polynomials, Rev. Acad. Canaria Cienc. 14 (2002), 25–34. [38] H. M. Srivastava and C. M. Joshi, Integral representation for the product of a class of generalized hypergeometric polynomials, Acad. Roy. Belg. Bull. Cl. Sci. (Ser. 5) 60 (1974), 919–926. [39] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984. [40] H. M. Srivastava, M. A. ¨ Ozarslan and C. Kaanoglu, Some families of generating functions for a certain class of three-variable polynomials, Integral Transforms Spec. Funct. 21 (2010), 885–896. [41] H. M. Srivastava and M. C. Daoust, Certain generalized Neumann expansions associated with the Kamp´e de F´eriet function, Nederl. Akad. Wetensch. Indag. Math. 31 (1969), 449–457. [42] H. M. Srivastava and P. W. Karlsson, Multiple Gaussian hypergeometric series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985. [43] H. M. Srivastava and R. Panda, An integral representation for the product of two Jacobi polynomials, J. London Math. Soc. (Ser. 2) 12 (1976), 419–425. [44] H. M. Srivastava, A note on the integral representation for the product of two generalized Rice polynomials, Collect. Math. 24 (1973), 117–121. [45] G. Szeg¨o, Orthogonal Polynomials, Fourth edition, Amererican Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, Rhode Island, 1975. [46] G. N. Watson, A note on the polynomials of Hermite and Laguerre, J. London Math. Soc. (1938) s1-13 (3), 204–209. [47] G. N. Watson, A note on the polynomials of Hermite and Laguerre, London Math. Soc, 13 (1938), 204–209. [48] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions, Fourth edition, Cambridge University Press, Cambridge, London and New York, 1927.; U0002-2206201220451900; http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/87458Test; http://tkuir.lib.tku.edu.tw:8080/dspace/bitstream/987654321/87458/-1/index.htmlTest

الإتاحة: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/87458Test
http://tkuir.lib.tku.edu.tw:8080/dspace/bitstream/987654321/87458/-1/index.htmlTest

المؤلفون: Liu, Shuoh-Jung, Chyan, Chuan-Jen, Lu, Han-Chun, Srivastava, H.M.

المساهمون: 淡江大學數學學系

مصطلحات موضوعية: Hypergeometric polynomials, Integral representations, Srivastava polynomials, Gamma function, Eulerian beta integral, Linearization relationship, Lagrange–Hermite polynomials, Pochhammer symbol, Hermite–Kampé de Fériet polynomials

العلاقة: Mathematical and Computer Modelling 54(5-6), pp.1420-1427; http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/72345Test; http://tkuir.lib.tku.edu.tw:8080/dspace/bitstream/987654321/72345/2/0895-7177_54Test(5-6)p1420-1427.pdf; http://tkuir.lib.tku.edu.tw:8080/dspace/bitstream/987654321/72345/-1/0895-7177_54Test(5-6)p1420-1427.pdf

الإتاحة: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/72345Test
http://tkuir.lib.tku.edu.tw:8080/dspace/bitstream/987654321/72345/2/0895-7177_54Test(5-6)p1420-1427.pdf
http://tkuir.lib.tku.edu.tw:8080/dspace/bitstream/987654321/72345/-1/0895-7177_54Test(5-6)p1420-1427.pdf