Fibonacci and Lucas Numbers with Applications, Volume 2

Name: Fibonacci and Lucas Numbers with Applications, Volume 2
Brand: Wiley
Price: 107.99 EUR
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Thomas Koshy(Autor*in)

Wiley (Verlag)

2. Auflage

Erschienen am 13. Dezember 2018

752 Seiten

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Inhalt

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-Matrix
32.2 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 Revisited
34.4 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 Revisited
37.3 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 Formulas
chapter 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
43.1 Bivariate Gibonacci Polynomials
43.2 Bivariate Fibonacci and Lucas Identities
43.3 Candido's Identity Revisited
chapter 44 Jacobsthal Family
44.1 Jacobsthal Family
44.2 Jacobsthal Occurrences
44.3 Jacobsthal Compositions
44.4 Triangular Numbers in the Family
44.5 Formal Languages
44.6 A USA Olympiad Delight
44.7 A Story of 1, 2, 7, 42, 429,...
44.8 Convolutions
chapter 45 Jacobsthal Tilings and Graphs
45.1 1 x n Tilings
45.2 2 x n Tilings
45.3 2 x n Tubular Tilings
45.4 3 x n Tilings
45.5 Graph-Theoretic Models
45.6 Digraph Models
chapter 46 Bivariate Tiling Models
46.1 A Model for f n(x,y)
46.2 Breakability
46.3 Colored Tilings
46.4 A Model for l n(x,y)
46.5 Colored Tilings Revisited
46.6 Circular Tilings Again
chapter 47 Vieta Polynomials
47.1 Vieta Polynomials
47.2 Aurifeuille's Identity
47.3 Vieta-Chebyshev Bridges
47.4 Jacobsthal-Chebyshev Links
47.5 Two Charming Vieta Identities
47.6 Tiling Models for V n
47.7 Tiling Models for v n(x)
chapter 48 Bivariate Gibonacci Family II
48.1 Bivariate Identities
48.2 Additional Bivariate Identities
48.3 A Bivariate Lucas Counterpart
48.4 A Summation Formula for f 2n(x,y)
48.5 A Summation Formula for l 2n(x,y)
48.6 Bivariate Fibonacci Links
48.7 Bivariate Lucas Links
chapter 49 Tribonacci Polynomials
49.1 Tribonacci Numbers
49.2 Compositions with Summands 1, 2, and 3
49.3 Tribonacci Polynomials
49.4 A Combinatorial Model
49.5 Tribonacci Polynomials and the Q-Matrix
49.6 Tribonacci Walks
49.7 A Bijection Between the Two Models
Appendix
A.1. The First 100 Fibonacci and Lucas Numbers
A.2 The First 100 Pell and Pell-Lucas Numbers
A.3 The First 100 Jacobsthal and Jacobsthal-Lucas Numbers
A.4 The First 100 Tribonacci Numbers
Abbreviations
Bibliography
Solutions to Odd-Numbered Exercises
Index

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