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Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes–Rogers and Thron–Rogers Polynomials, with Coefficientwise Hankel-Total Positivity
Alan D. Sokal
:
University College London, London, United Kingdom and New York University, New York , New York
Bao-Xuan Zhu
:
University College London, London, United Kingdom and Jiangsu Normal University, Xuzhou, People’s Republic of China
| Softcover ISBN: | 978-1-4704-6268-0 |
| Product Code: | MEMO/291/1450 |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-7683-0 |
| Product Code: | MEMO/291/1450.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-6268-0 |
| eBook: ISBN: | 978-1-4704-7683-0 |
| Product Code: | MEMO/291/1450.B |
| List Price: | $170.00 $127.50 |
| MAA Member Price: | $153.00 $114.75 |
| AMS Member Price: | $136.00 $102.00 |
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Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes–Rogers and Thron–Rogers Polynomials, with Coefficientwise Hankel-Total Positivity
Alan D. Sokal
:
University College London, London, United Kingdom and New York University, New York , New York
Bao-Xuan Zhu
:
University College London, London, United Kingdom and Jiangsu Normal University, Xuzhou, People’s Republic of China
| Softcover ISBN: | 978-1-4704-6268-0 |
| Product Code: | MEMO/291/1450 |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-7683-0 |
| Product Code: | MEMO/291/1450.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-6268-0 |
| eBook ISBN: | 978-1-4704-7683-0 |
| Product Code: | MEMO/291/1450.B |
| List Price: | $170.00 $127.50 |
| MAA Member Price: | $153.00 $114.75 |
| AMS Member Price: | $136.00 $102.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 291; 2023; 154 ppMSC: Primary 05; Secondary 30; 15
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Table of Contents
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Chapters
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1. Introduction
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2. The $\boldsymbol {m}$-Stieltjes–Rogers and $\boldsymbol {m}$-Thron–Rogers polynomials
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3. Relation between different values of $\boldsymbol {m}$
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4. The $\boldsymbol {m}$-Jacobi–Rogers polynomials
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5. The generalized $\boldsymbol {m}$-Stieltjes–Rogers, $\boldsymbol {m}$-Thron–Rogers and $\boldsymbol {m}$-Jacobi–Rogers polynomials
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6. Generalized $\boldsymbol {m}$-Jacobi–Rogers polynomials in terms of ordered trees and forests
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7. Contraction formulae for $\boldsymbol {m}$-branched continued fractions
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8. Production matrices
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9. Total positivity
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10. Weights periodic of period $\boldsymbol {m\!+\!1}$ or $\boldsymbol {m}$
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11. Weights eventually periodic of period $\boldsymbol {m\!+\!1}$ or $\boldsymbol {m}$
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12. Weights quasi-affine or factorized of period ${\boldsymbol {m\!+\!1}}$ or $\boldsymbol {m}$
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13. Ratios of contiguous hypergeometric series I: $\boldsymbol { {{}_{m+1 \!}{F}{_{0}}\!} }$
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14. Ratios of contiguous hypergeometric series II: $\boldsymbol { {{}_{r }{F}{_{s}}\!} }$
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15. Ratios of contiguous hypergeometric series III: $\boldsymbol { {_{r}{\phi }{_{s}}} }$
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16. Some final remarks
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Additional Material
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
Volume: 291; 2023; 154 pp
MSC: Primary 05; Secondary 30; 15
-
Chapters
-
1. Introduction
-
2. The $\boldsymbol {m}$-Stieltjes–Rogers and $\boldsymbol {m}$-Thron–Rogers polynomials
-
3. Relation between different values of $\boldsymbol {m}$
-
4. The $\boldsymbol {m}$-Jacobi–Rogers polynomials
-
5. The generalized $\boldsymbol {m}$-Stieltjes–Rogers, $\boldsymbol {m}$-Thron–Rogers and $\boldsymbol {m}$-Jacobi–Rogers polynomials
-
6. Generalized $\boldsymbol {m}$-Jacobi–Rogers polynomials in terms of ordered trees and forests
-
7. Contraction formulae for $\boldsymbol {m}$-branched continued fractions
-
8. Production matrices
-
9. Total positivity
-
10. Weights periodic of period $\boldsymbol {m\!+\!1}$ or $\boldsymbol {m}$
-
11. Weights eventually periodic of period $\boldsymbol {m\!+\!1}$ or $\boldsymbol {m}$
-
12. Weights quasi-affine or factorized of period ${\boldsymbol {m\!+\!1}}$ or $\boldsymbol {m}$
-
13. Ratios of contiguous hypergeometric series I: $\boldsymbol { {{}_{m+1 \!}{F}{_{0}}\!} }$
-
14. Ratios of contiguous hypergeometric series II: $\boldsymbol { {{}_{r }{F}{_{s}}\!} }$
-
15. Ratios of contiguous hypergeometric series III: $\boldsymbol { {_{r}{\phi }{_{s}}} }$
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16. Some final remarks
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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