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On trigonometric-like decompositions of functions with respect to the cyclic group of order n

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The cyclic group labelled family of α-projection operators implicitly present in [28] is used as in [5]-[9], [23] for investigation of decomposition of functions with respect to the cyclic group of order n. Series of new identities thus arising are demonstrated and new perspectives for further investigation are indicated as for example in the case of q-extended special polynomials. The paper constitutes an example of the application of the method of projections introduced in [26]; see also references [5]-[9].
Wydawca
Rocznik
Strony
111--127
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
  • Institute of Computer Science Białystok University Ul. Sosnowa 64 15-887 Białystok, Poland
  • Institute of Mathematics, Bialystok University, ul.Sosnowa 64, 15-887 Bialystok, POLAND
Bibliografia
  • [1] Bajguz, W., Kwasniewski, A. K., On generalization of Lucas symmetric functions and Tchebycheff polynomials, Integral Transform. Spec. Func. 8(3-4) (1999), 165-174.
  • [2] Bajguz, W., Kwasniewski, A. K., On hyperbolic quasi-numbers and Chebyshev-like functions, Rep. Math. Phys. 43(3) (1999), 367-376.
  • [3] Bajguz, W., On generalization Tchebycheff polynomials, Integral Transform. Spec. Func. 1(2) (2000), 91-98.
  • [4] Bateman, H., Erdéley, A., Higher Transcendental Functions, Vol. Ill, Chapter 18, MC Graw-Hill Book Company, Inc., New York, 1953, 212-217.
  • [5] Ben Cheikh, Y., Decomposition of Bessel functions with respect to the cyclic group of order n, Matematiche (Catania) 52 (1997), 365-378.
  • [6] Ben Cheikh, Y., Decomposition of Laguerre polynomials with respect to the cyclic group of order n, J. Comput. Appl. Math. 99 (1998), 55-66.
  • [7] Ben Cheikh, Y., Decomposition of theBoas-Buck polynomials with respect to the cyclic group of order n Ann. Univ. Mariae Curie-Sklodowska Sect. A 52(2) (1998), 15-27
  • [8] Ben Cheikh, Y., Differential equations satisfied by components with respect to the cyclic group of oreder n of some special functions J. Math. Anal. Appl. 244 (2000), 483-497.
  • [9] Ben Cheikh, Y., Decomposition of some complex functions with respect to the cyclic group of order n, Appl. Math. Inform. 4(2) (2000), 30-53.
  • [10] Davis, P. J., Circulant Matrices, John Wiley & Sons Inc., New York, 1979
  • [11] Gasper, G., Rahman, M., Basic Hypergeometric Series, Cambridge Univ. Press, Cambridge, 1990.
  • [12] Good, I. J., A simple generalization of analytic function theory, Exposition. Math. 6 (1988), 289-311.
  • [13] Jackson, F.H., On q-differenc equations, Amer. J. Math. 32 (1910), 305-314.
  • [14] Jackson, F. H., On q-define integrals, Quart. J. Pure Appl. Math. 41 (1910), 193-203.
  • [15] Jackson, F.H., A q-generalization of Abel series, Rend. Palermo 29 (1910), 340-346.
  • [16] Kassel, Ch., Quantum Groups, Springer-Verlag, New York, 1995.
  • [17] Kwasniewski, A. K., Zadania do wyktadu z algebry, Wyd. Uniw. Wroc., Wroclaw, 1985.
  • [18] Kwasniewski, A. K., On the Onsager problem for Potts models, J. Phys. A 19 (1986), 1469-1476.
  • [19] Kwasniewski, A. K., On hyperbolic and elliptic mappings and quasi-number algebras, Adv. Appl. Clifford Algebras 2 (1992), 107-144.
  • [20] Kwasniewski, A. K., Czech, R., On quasi-number algebras, Rep. Math. Phys. 31(3), (1992), 241-251.
  • [21] Kwasniewski, A. K., On peculiarity of the p = 2 case among the p-state Ising-like models, Rep. Math. Phys. 43(3) (1991), 367-376.
  • [22] Kwasniewski, A. K., et al., On quantum mechanics and generalized Clifford algebras, Adv. Appl. Clifford Algebras 8(2) (1998), 417-432.
  • [23] Kwasniewski, A. K., Higher order recurrences for analytical functions of Tchebysheff type, Adv. Appl. Clifford Algebras 9(1) (1999), 41-54.
  • [24] Kwasniewski, A. K., On extended finite operator calculus of Rota and quantum groups Integral Transform. Spec. Func. 2(4) (2001), 333-340.
  • [25] Kwasniewski, A. K., Towards ip extension of Rota’s finite operator calculus, Rep. Math. Phys. 48 (3) (2001), 305-342.
  • [26] Muldoon, M. E., Ungar, A. A., Beyond sin and cos, Math. Mag. 69(1) (1996), 3-14.
  • [27] Ricci, P. E., Le funzioni pseudo-iperboliche e pseudo-trigonometr, Pubbl. Istit. Mat. Appl. Fac. Ingr. Univ. Stud. Roma Quaderno 2 (1978), 37-49.
  • [28] Ungar, A. A., Higher order a-hyperbolic functions, Indian J. Pure Appl. Math. 15(3) (1984), 301-304.
  • [29] Viskov, O. V., Operator characterization of generalized Appel polynomials, Soviet Math. Dokl. 16 (1975), 1521-1524.
  • [30] Viskov, O. V., On the basis in the space of polynomials, Soviet Math. Dokl. 19 (1978), 250-253.
  • [31] Wilf, H. S., Generating Functionology, Academic Press, Inc., Boston, 1990.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0014-0007
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