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Fibonacci and Lucas numbers with applications /
Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this boo...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
Wiley & Sons,
[2018]-
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| Edición: | Second edition. |
| Colección: | Pure and applied mathematics: a Wiley series of texts, monographs, and tracts
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title Page; Copyright; Contents; List of Symbols; Preface; chapter 31 Fibonacci and Lucas Polynomials I; 31.1 Fibonacci and Lucas Polynomials; 31.2 Pascal's Triangle; 31.3 Additional Explicit Formulas; 31.4 Ends of the Numbers l n; 31.5 Generating Functions; 31.6 Pell and Pell-Lucas Polynomials; 31.7 Composition of Lucas Polynomials; 31.8 De Moivre-like Formulas; 31.9 Fibonacci-Lucas Bridges; 31.10 Applications of Identity (31.51); 31.11 Infinite Products; 31.12 Putnam Delight Revisited; 31.13 Infinite Simple Continued Fraction; chapter 32 Fibonacci and Lucas Polynomials II.
- 32.1 Q-Matrix32.2 Summation Formulas; 32.3 Addition Formulas; 32.4 A Recurrence for f n 2; 32.5 Divisibility Properties; chapter 33 Combinatorial Models II; 33.1 A Model for Fibonacci Polynomials; 33.2 Breakability; 33.3 A Ladder Model; 33.4 A Model for Pell-Lucas Polynomials: Linear Boards; 33.5 Colored Tilings; 33.6 A New Tiling Scheme; 33.7 A Model for Pell-Lucas Polynomials: Circular Boards; 33.8 A Domino Model for Fibonacci Polynomials; 33.9 Another Model for Fibonacci Polynomials; chapter 34 Graph-Theoretic Models II; 34.1 Q-Matrix and Connected Graph; 34.2 Weighted Paths.
- 34.3 Q-Matrix Revisited34.4 Byproducts of the Model; 34.5 A Bijection Algorithm; 34.6 Fibonacci and Lucas Sums; 34.7 Fibonacci Walks; chapter 35 Gibonacci Polynomials; 35.1 Gibonacci Polynomials; 35.2 Differences of Gibonacci Products; 35.3 Generalized Lucas and Ginsburg Identities; 35.4 Gibonacci and Geometry; 35.5 Additional Recurrences; 35.6 Pythagorean Triples; chapter 36 Gibonacci Sums; 36.1 Gibonacci Sums; 36.2 Weighted Sums; 36.3 Exponential Generating Functions; 36.4 Infinite Gibonacci Sums; chapter 37 Additional Gibonacci Delights; 37.1 Some Fundamental Identities Revisited.
- 37.2 Lucas and Ginsburg Identities Revisited37.3 Fibonomial Coefficients; 37.4 Gibonomial Coefficients; 37.5 Additional Identities; 37.6 Strazdins' Identity; chapter 38 Fibonacci and Lucas Polynomials III; 38.1 Seiffert's Formulas; 38.2 Additional Formulas; 38.3 Legendre Polynomials; chapter 39 Gibonacci Determinants; 39.1 A Circulant Determinant; 39.2 A Hybrid Determinant; 39.3 Basin's Determinant; 39.4 Lower Hessenberg Matrices; 39.5 Determinant with a Prescribed First Row; chapter 40 Fibonometry II; 40.1 Fibonometric Results; 40.2 Hyperbolic Functions.
- 40.3 Inverse Hyperbolic Summation Formulaschapter 41 Chebyshev Polynomials; 41.1 Chebyshev Polynomials T n(x); 41.2 T n(x) and Trigonometry; 41.3 Hidden Treasures in Table 41.1; 41.4 Chebyshev Polynomials U n(x); 41.5 Pell's Equation; 41.6 U n(x) and Trigonometry; 41.7 Addition and Cassini-like Formulas; 41.8 Hidden Treasures in Table 41.8; 41.9 A Chebyshev Bridge; 41.10 T n and U n as Products; 41.11 Generating Functions; chapter 42 Chebyshev Tilings; 42.1 Combinatorial Models for U n; 42.2 Combinatorial Models for T n; 42.3 Circular Tilings; chapter 43 Bivariate Gibonacci Family I.