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Incomplete Bivariate Fibonacci and Lucas ð ‘ -Polynomials

Author

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  • Dursun Tasci
  • Mirac Cetin Firengiz
  • Naim Tuglu

Abstract

We define the incomplete bivariate Fibonacci and Lucas ð ‘ - polynomials. In the case ð ‘¥ = 1 , 𠑦 = 1 , we obtain the incomplete Fibonacci and Lucas ð ‘ - numbers. If ð ‘¥ = 2 , 𠑦 = 1 , we have the incomplete Pell and Pell-Lucas ð ‘ - numbers. On choosing ð ‘¥ = 1 , 𠑦 = 2 , we get the incomplete generalized Jacobsthal number and besides for ð ‘ = 1 the incomplete generalized Jacobsthal-Lucas numbers. In the case ð ‘¥ = 1 , 𠑦 = 1 , ð ‘ = 1 , we have the incomplete Fibonacci and Lucas numbers. If ð ‘¥ = 1 , 𠑦 = 1 , ð ‘ = 1 , 𠑘 = ⌊ ( ð ‘› − 1 ) / ( ð ‘ + 1 ) ⌋ , we obtain the Fibonacci and Lucas numbers. Also generating function and properties of the incomplete bivariate Fibonacci and Lucas ð ‘ - polynomials are given.

Suggested Citation

  • Dursun Tasci & Mirac Cetin Firengiz & Naim Tuglu, 2012. "Incomplete Bivariate Fibonacci and Lucas ð ‘ -Polynomials," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-11, April.
    • Handle: RePEc:hin:jnddns:840345
    DOI: 10.1155/2012/840345
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    Cited by:

    1. Elen Viviani Pereira Spreafico & Eudes Antonio Costa & Paula Catarino, 2024. "On the Incomplete Edouard and Incomplete Edouard–Lucas Numbers," Mathematics, MDPI, vol. 12(21), pages 1-9, October.

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