Applications of Continuous Fractions in Orthogonal Polynomials

• Ana Cláudia Marassá Roza Boso

  Master in Irrigation and Drainage, Faculty of Agronomic Sciences - UNESP, Botucatu Campus

  Author

• Luís Roberto Almeida Gabriel Filho

  Professor at the State University of São Paulo - UNESP

  Author

• Camila Pires Cremasco Gabriel

  Professor at the State University of São Paulo - UNESP

  Author

• Bruno César Góes

  Master's Degree in Agribusiness and Development, Faculty of Sciences and Engineering - UNESP, Campus de Tupã

  Author

• Fernando Ferrari Putti

  Professor at the State University of São Paulo - UNESP

  Author

Several applications of continuous fractions are restricted to theoretical studies, such as problems associated with the approximation of functions, determination of rational and irrational numbers, applications in physics in determining the resistance of electric circuits and integral equations and in several other areas of mathematics. This work aimed to study the results that open the way for the connection of continuous fractions with the orthogonal polynomials. As support, we will study the general case, where the applications of the Wallis formulas in a monolithic orthogonal polynomial, which generates a continuous fraction of the Jacobi type. It will be allowed applications with relations of recurrence of three terms in the polynomials of Tchebyshev and Legendre, through the results found, establishing connection between them with the continuous fractions. And finally, will be presented the "Number of gold", that is an application of this theory.

1. Ana Cláudia Marassá Roza Boso, Master in Irrigation and Drainage, Faculty of Agronomic Sciences - UNESP, Botucatu Campus

   Department of Agronomy, Irrigation and Drainage, Univ. State University of São Paulo - UNESP, Botucatu, Sao Paulo, Brazil

2. Luís Roberto Almeida Gabriel Filho, Professor at the State University of São Paulo - UNESP

   Department of Applied Mathematics, Univ. State University of São Paulo - UNESP, Tupã, Sao Paulo, Brazil

3. Camila Pires Cremasco Gabriel, Professor at the State University of São Paulo - UNESP

   Department of Biosystems Engineering, Univ. State University of São Paulo - UNESP, Tupã, Sao Paulo, Brazil

4. Bruno César Góes, Master's Degree in Agribusiness and Development, Faculty of Sciences and Engineering - UNESP, Campus de Tupã

   Departamento de Matemática Aplicada, Univ. Universidade Estadual Paulista - UNESP, Tupã, São Paulo, Brasil

5. Fernando Ferrari Putti, Professor at the State University of São Paulo - UNESP

   Department of Biosystems Engineering, Univ. State University of São Paulo - UNESP, Tupã, Sao Paulo, Brazil

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Copyright (c) 2018 Ana Cláudia Marassá Roza Boso, Luís Roberto Almeida Gabriel Filho, Camila Pires Cremasco Gabriel, Bruno César Góes, Fernando Ferrari Putti

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