Some results on convolved (p, q)-Fibonacci polynomials

References

• Cheon GS, Kim H, Shapiro LW. A generalization of Lucas polynomial sequence. Discrete Appl Math. 2009;157(5):920–927. doi: 10.1016/j.dam.2008.03.034
   Web of Science ®Google Scholar
• He TX, Shiue PJS. On sequences of numbers and polynomials defined by linear recurrence relations of order 2. Int J Math Math Sci. 2009;21 pp. Art. ID 709386.
   Google Scholar
• Horadam AF. A synthesis of certain polynomial sequences. In: Bergum GE, Philippou AN, Horadam AF, editors. Applications of Fibonacci numbers, Vol. 6. Dordrecht: Kluwer Academic Publishers; 1996. p. 215–229.
   Google Scholar
• Hsu LC. On stirling-type pairs and extended Gegenbauer-Humbert-Fibonacci polynomials. In: Bergum GE, Philippou AN, Horadam AF, editors. Applications of Fibonacci numbers, Vol. 5. Dordrecht: Kluwer Academic Publishers; 1993. p. 367–377.
   Google Scholar
• Hsu LC, Shiue PJS. Cycle indicators and special functions. Ann Comb. 2001;5(2):179–196. doi: 10.1007/PL00001299
   Google Scholar
• Lee G, Asci M. Some properties of the (p, q)-Fibonacci and (p, q)-Lucas polynomials. J Appl Math. 2012;18 pp. Art. ID 264842.
   Google Scholar
• Wang J. Some new results for the (p, q)-Fibonacci and Lucas polynomials. Adv Differ Equ. 2014;2014:64. 15 pp. doi: 10.1186/1687-1847-2014-64
   Web of Science ®Google Scholar
• Bolat C, Köse H. On the properties of k-Fibonacci numbers. Int J Contemp Math Sci. 2010;5(21–24):1097–1105.
   Google Scholar
• Falcón S. On the k-Lucas numbers. Int J Contemp Math Sci. 2011;6(21–24):1039–1050.
   Google Scholar
• Falcón S, Plaza Á. On the Fibonacci k-numbers. Chaos Solitons Fractals. 2007;32(5):1615–1624. doi: 10.1016/j.chaos.2006.09.022
   Web of Science ®Google Scholar
• Nalli A, Haukkanen P. On generalized Fibonacci and Lucas polynomials. Chaos Solitons Fractals. 2009;42(5):3179–3186. doi: 10.1016/j.chaos.2009.04.048
   Web of Science ®Google Scholar
• Dilcher K. A generalization of Fibonacci polynomials and a representation of Gegenbauer polynomials of integer order. Fibonacci Quart. 1987;25(4):300–303.
   Google Scholar
• Feng H, Zhang Z. Computational formulas for convoluted generalized Fibonacci and Lucas numbers. Fibonacci Quart. 2003;41(2):144–151.
   Google Scholar
• Hoggatt Jr VE. Convolution triangles for generalized Fibonacci numbers. Fibonacci Quart. 1970;8(2):158–171.
   Google Scholar
• Hoggatt Jr VE, Bicknell-Johnson M. Fibonacci convolution sequences. Fibonacci Quart. 1977;15(2):117–122.
   Google Scholar
• Horadam AF, Mahon JM. Convolutions for Pell polynomials. In: Philippou AN, Bergum GE, Horadam AF, editors. Fibonacci numbers and their applications. Dordrecht: Reidel; 1986. p. 55–80.
   Google Scholar
• Horadam AF, Mahon JM. Mixed Pell polynomials. Fibonacci Quart. 1987;25(4):291–299.
   Google Scholar
• Liu G. Formulas for convolution Fibonacci numbers and polynomials. Fibonacci Quart. 2002;40(4):352–357.
   Google Scholar
• Moree P. Convoluted convolved Fibonacci numbers. J Integer Seq. 2004;7(2):14 pp. Article 04.2.2.
   Google Scholar
• Ramírez JL. Some properties of convolved k-Fibonacci numbers. ISRN Combin. 2013;5 pp. Art. ID 759641.
   Google Scholar
• Ramírez JL. On convolved generalized Fibonacci and Lucas polynomials. Appl Math Comput. 2014;229:208–213. doi: 10.1016/j.amc.2013.12.049
   Web of Science ®Google Scholar
• Yuan Y, Zhang W. Some identities involving the Fibonacci polynomials. Fibonacci Quart. 2002;40(4):314–318.
   Web of Science ®Google Scholar
• Zhang W. Some identities involving the Fibonacci numbers. Fibonacci Quart. 1997;35(3):225–229.
   Google Scholar
• Zhao FZ, Wang T. Some identities involving the powers of the generalized Fibonacci numbers. Fibonacci Quart. 2003;41(1):7–12.
   Google Scholar
• Gould HW. Inverse series relations and other expansions involving Humbert polynomials. Duke Math J. 1965;32:697–711. doi: 10.1215/S0012-7094-65-03275-8
   Web of Science ®Google Scholar
• Abramowitz M, Stegun IA. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover Publications; 1992. Reprint of the 1972 edition.
   Google Scholar
• Rainville ED. Special functions. Bronx, NY: Chelsea Publishing; 1971. Reprint of 1960 first edition.
   Google Scholar
• Comtet L. Advanced combinatorics. Dordrecht: D. Reidel Publishing; 1974.
   Google Scholar
• Riordan J. An introduction to combinatorial analysis. Mineola, NY: Dover Publications; 2002. Reprint of the 1958 original.
   Google Scholar
• Sun ZH. On the properties of Newton-Euler pairs. J Number Theory. 2005;114(1):88–123. doi: 10.1016/j.jnt.2005.05.004
   Web of Science ®Google Scholar
• Janjić M. Hessenberg matrices and integer sequences. J Integer Seq. 2010;13(7):10 pp. Article 10.7.8.
   Google Scholar
• Janjić M. Determinants and recurrence sequences. J Integer Seq. 2012;15(3):21 pp. Article 12.3.5.
   Google Scholar
• Jacobson N. Basic algebra. I. 2nd ed. New York: W.H. Freeman and Company; 1985.
   Google Scholar