On generating functions of biorthogonal polynomials suggested by the Laguerre polynomials

• Samanta, K. P. ^[1] ; Chongdar, A. K. ^[1]
  1. [1] Bengal Engineering and Science University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 33, Nº. 2, 2014, págs. 133-146
• Idioma: inglés
• DOI: 10.4067/S0716-09172014000200001
• Enlaces
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• Resumen

  • In this note, we have obtained some novel bilateral generating functions involving Konhauser biorthogonal polynomials,  which is converted into trilateral generating functions with Tchebycheff polynomials by group theoretic method. As special cases, we have obtained the corresponding results on generalised Laguerre polynomials. Some applications are also given here.

• Referencias bibliográficas
  • Citas [1] Konhauser, J. D. E., Some properties of biorthogonal polynomials, J.‏ Math. Anal. Appl., 11 , pp. 242-260, (1965).‏
  • [2] Konhauser, J. D. E., Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math., 21, pp. 303-314, (1967).‏
  • [3] Spencer, L. and Fano, U., Penetration and diffusion of X-rays , calculation of spatial distribution by polynomial expansion, J. Res. Nat.‏...
  • [4] Erdelyi, Arthur, with Magnus, W., Oberhettinger, F., Tricomi, F. G.,‏ et al., Higher transcendental function, vol. 2. New York: McGraw-Hill,‏...
  • [5] Carlitz, L., A note on certain biorthogonal polynomials, Pacific J.‏ Math., 24, pp. 425-430 (1968).‏
  • [6] Carlitz, L., A note on the Laguerre polynomials, Michigan Math. J.,‏ 7(3), pp. 219-223, (1960).‏
  • [7] Al-Salam, W. A., Operational representations for the Laguerre and‏ other polynomials, Duke Math. Jour., 31, pp. 127-142, (1964).‏
  • [8] Calvez, L. C. et Genin, R., Applications des relations entre les fonctions generatrices et les formules de type Rodrigues, C. R. Acad....
  • [9] Andrews,L.C., Special for Engineers and Applied Mathematicians,‏ Macmillan Publishing Company.‏
  • [10] Prabhakar, T. R., On a set of polynomials suggested by the Laguerre‏ polynomials, Pacific J. Math., 35 , pp. 213-219, (1970).‏
  • [11] Prabhakar, T. R., On the other set of biorthogonal polynomials suggested by Laguerre polynomials, Pacific J. Math., 37, pp. 801-804,‏...
  • [12] Srivastava, H. M., Some Biorthogonal polynomials suggested by the‏ Laguerre polynomials, Pacific J. Math., 98, pp. 235-250, (1982).‏
  • [13] Srivastava, H. M., A note on the Konhauser sets of Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math.,...
  • [14] Srivastava, A. N. and Singh, S. N., On the Konhauser polynomials‏ Y α‏ n (x; k), Indian J. pure appl. Math., 10, pp. 1121-1126, (1979).‏
  • [15] Shreshtha, R.M. and Bajracharya, S., Group theoretical study of a‏ bilateral generating function, Int. Trans. and Spec. func., 5(1-2),...
  • [16] Truesdell, C., An essay toward a unified theory of special functions,‏ Princeton university press, (1948).‏
  • [17] McBride, E. B., Obtaining Generating Functions, Springer Verlag,‏ Berlin, (1972).‏
  • [18] Sharma, R. and Chongdar, A. K., Some generating functions of Laguerre polynomials from the lie group view point, Bull. Cal. Math.‏ Soc.,...
  • [19] Alam, S. and Chongdar, A. K., On generating functions of modified‏ Laguerre polynomials, Rev. Real Academia de Ciencias Zaragoza, 62,‏...
  • [20] Das, S. and Chatterjea, S. K., On a partial differential operator for‏ Laguerre polynomials, Pure Math. Manuscript,4, pp. 187-193, (1985).‏
  • [21] Chongdar, A. K., Some generating functions involving Laguerre polynomials, Bull. Cal. Math. Soc., 76, pp. 262-269, (1984).‏
  • [22] Patil, K. R. and Thakare, N. K., Multilinear generating function for‏ the Konhauser biorthogonal polynomial sets,SIAM J. Math. Anal.,...