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On Stirling-Type Pairs and Extended Gegenbauer-Humbert-Fibonacci Polynomials

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Applications of Fibonacci Numbers

Abstract

Throughout the paper use will be made of formal power series techniques. Several known theorems concerning power-type generating functions and potential polynomials will be employed as basic tools, some of which may,be found in Comtet [1] (see, in particular, chap.3, §3.5 and §3.8).

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References

  1. Comtet, L. Advanced Combinatorics. Dordrecht: Reidel, 1974.

    Book  MATH  Google Scholar 

  2. Dilcher, K. “A generalization of Fibonacci polynomials and a representation of Gegenbauer polynomials of integer order.” The Fibonacci Quarterly, Vol. 25.4 (1987): pp. 300–303.

    MathSciNet  MATH  Google Scholar 

  3. Gould, H.W. “Inverse series relations and other expansions involving Humbert polynomials.” Duke Math. J., Vol. 32.4 (1965): pp. 697–711.

    Article  MathSciNet  MATH  Google Scholar 

  4. Hoggatt, Jr, V.E. “Convolution triangles for generalized Fibonacci numbers.” The Fibonacci Quarterly, Vol. 8.2 (1970): pp. 158–171.

    MathSciNet  MATH  Google Scholar 

  5. Hoggatt, Jr., V.E. and Bicknell-Johnson, Marjorie. “Fibonacci convolution sequences.” The Fibonacci Quarterly, Vol. 15.2 (1977): pp. 117–122.

    MathSciNet  MATH  Google Scholar 

  6. Horadam, A.F. and Mahon (Bro), J.M. “Convolution for Pell polynomials.” Fibonacci Numbers and Their Applications. Edited by A.N. Philippou, G. E. Bergum and A. F. Horadam. Dordrecht, The Netherlands: D. Reidel Publ. Company (1986): pp. 55–80.

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  7. Horadam, A.F. and Mahon (Bro), J.M. “Mixed Pell polynomials.” The Fibonacci Quarterly, Vol. 25.4 (1987): pp. 291–299.

    MathSciNet  MATH  Google Scholar 

  8. Hsu, L.C. “A partition identity with certain applications.” Portugaliae Mathematica, Vol. 48.3 (1991): pp. 357–361.

    MathSciNet  MATH  Google Scholar 

  9. Hsu, L.C. and Chu, W. “A kind of asymptotic expansion using partitions.” Tôhoku Math. J., Vol. 43.2 (1991): pp. 235–242.

    Article  MathSciNet  MATH  Google Scholar 

  10. Hsu, L.C. “Generalized Stirling number pairs associated with inverse relations.” The Fibonacci Quarterly, Vol. 25.4 (1987): pp. 346–351.

    MathSciNet  MATH  Google Scholar 

  11. Hsu, L.C. “Theory and application of generalized Stirling number pairs.” J. Math. Res. & Exposition, Vol. 9.2 (1989): pp. 211–220.

    MathSciNet  MATH  Google Scholar 

  12. Robbins, N. “Some convolution-type and combinatorial identities pertaining to binary linear recurrences.” The Fibonacci Quarterly, Vol. 29.3 (1991): pp. 249–255.

    MathSciNet  MATH  Google Scholar 

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© 1993 Springer Science+Business Media Dordrecht

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Hsu, L.C. (1993). On Stirling-Type Pairs and Extended Gegenbauer-Humbert-Fibonacci Polynomials. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2058-6_34

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  • DOI: https://doi.org/10.1007/978-94-011-2058-6_34

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4912-2

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