New formulas including convolution, connection and radicals formulas of \(k\)-Fibonacci and \(k\)-Lucas polynomials

DOI10.1007/s13226-021-00214-5zbMath1501.11024OpenAlexW4210293559WikidataQ113899330 ScholiaQ113899330MaRDI QIDQ2095082

Waleed M. Abd-Elhameed, N. A. Zeyada

Publication date: 9 November 2022

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-021-00214-5

zbMATH Keywords

connection and linearization problemsconvolution identities\(k\)-Fibonacci polynomials\(k\)-Lucas polynomialsreduction of radicals

Mathematics Subject Classification ID

Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

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• On \(k\)-Fibonacci sequences and polynomials and their derivatives
• A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients
• On linearization coefficients of Jacobi polynomials
• Cardano's formula, square roots, Chebyshev polynomials and radicals
• A common generalization of convolved generalized Fibonacci and Lucas polynomials and its applications
• Generalized Lucas polynomial sequence approach for fractional differential equations
• Cardan polynomials, Chebyshev exponents, ultra-radicals and generalized imaginary units
• On the Fibonacci \(k\)-numbers
• Linearization formulae for certain Jacobi polynomials
• Cardan Polynomials and the Reduction of Radicals
• Simplification of Nested Radicals
• Radicals and units in Ramanujan's work
• Ramanujan's Association with Radicals in India
• A generalization of generalized Fibonacci and generalized Pell numbers
• New product and linearization formulae of Jacobi polynomials of certain parameters
• Quantum information entropies and orthogonal polynomials

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