Umbral Calculus

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Guide To The Umbral Calculus, A Different Mathematical Language

Author : Silvia Licciardi
Publisher : World Scientific
ISBN 13 : 9811255342
Total Pages : 295 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Guide To The Umbral Calculus, A Different Mathematical Language by : Silvia Licciardi

Download or read book Guide To The Umbral Calculus, A Different Mathematical Language written by Silvia Licciardi and published by World Scientific. This book was released on 2022-06-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers different aspects of umbral calculus and of its more recent developments. It discusses the technical details in depth, including its relevant applications. The book has therefore manyfold scopes to introduce a mathematical tool, not widespread known as it should be; to present a complete account of the relevant capabilities through the use of different examples of applications; to provide a formal bridge between different fields of research in pure and applied.

Umbral Calculus

Author : Steven Roman
Publisher : Courier Dover Publications
ISBN 13 : 0486834131
Total Pages : 209 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Umbral Calculus by : Steven Roman

Download or read book Umbral Calculus written by Steven Roman and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. The text focuses on classical umbral calculus, which dates back to the 1850s and continues to receive the attention of modern mathematicians. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial convolution. The final chapter offers a glimpse of the newer and less well-established forms of umbral calculus.

Modern Umbral Calculus

Author : Francesco Aldo Costabile
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110650096
Total Pages : 275 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Modern Umbral Calculus by : Francesco Aldo Costabile

Download or read book Modern Umbral Calculus written by Francesco Aldo Costabile and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel approach to umbral calculus, which uses only elementary linear algebra (matrix calculus) based on the observation that there is an isomorphism between Sheffer polynomials and Riordan matrices, and that Sheffer polynomials can be expressed in terms of determinants. Additionally, applications to linear interpolation and operator approximation theory are presented in many settings related to various families of polynomials.

Modern Umbral Calculus

Author : Francesco Aldo Costabile
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110652927
Total Pages : 276 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Modern Umbral Calculus by : Francesco Aldo Costabile

Download or read book Modern Umbral Calculus written by Francesco Aldo Costabile and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel approach to umbral calculus, which uses only elementary linear algebra (matrix calculus) based on the observation that there is an isomorphism between Sheffer polynomials and Riordan matrices, and that Sheffer polynomials can be expressed in terms of determinants. Additionally, applications to linear interpolation and operator approximation theory are presented in many settings related to various families of polynomials.

Umbral Calculus and Hopf Algebras

Author : Robert A. Morris
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Umbral Calculus and Hopf Algebras by : Robert A. Morris

Download or read book Umbral Calculus and Hopf Algebras written by Robert A. Morris and published by . This book was released on 1982 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Gian-Carlo Rota on Analysis and Probability

Author : Jean Dhombres
Publisher : Springer Science & Business Media
ISBN 13 : 9780817642754
Total Pages : 424 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Gian-Carlo Rota on Analysis and Probability by : Jean Dhombres

Download or read book Gian-Carlo Rota on Analysis and Probability written by Jean Dhombres and published by Springer Science & Business Media. This book was released on 2002-12-06 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gian-Carlo Rota was born in Vigevano, Italy, in 1932. He died in Cambridge, Mas sachusetts, in 1999. He had several careers, most notably as a mathematician, but also as a philosopher and a consultant to the United States government. His mathe matical career was equally varied. His early mathematical studies were at Princeton (1950 to 1953) and Yale (1953 to 1956). In 1956, he completed his doctoral thesis under the direction of Jacob T. Schwartz. This thesis was published as the pa per "Extension theory of differential operators I", the first paper reprinted in this volume. Rota's early work was in analysis, more specifically, in operator theory, differ ential equations, ergodic theory, and probability theory. In the 1960's, Rota was motivated by problems in fluctuation theory to study some operator identities of Glen Baxter (see [7]). Together with other problems in probability theory, this led Rota to study combinatorics. His series of papers, "On the foundations of combi natorial theory", led to a fundamental re-evaluation of the subject. Later, in the 1990's, Rota returned to some of the problems in analysis and probability theory which motivated his work in combinatorics. This was his intention all along, and his early death robbed mathematics of his unique perspective on linkages between the discrete and the continuous. Glimpses of his new research programs can be found in [2,3,6,9,10].

Multivariate Umbral Calculus

Author : Christopher Parrish
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Multivariate Umbral Calculus by : Christopher Parrish

Download or read book Multivariate Umbral Calculus written by Christopher Parrish and published by . This book was released on 1974 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Comprehensive Treatment of q-Calculus

Author : Thomas Ernst
Publisher : Springer Science & Business Media
ISBN 13 : 303480430X
Total Pages : 491 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis A Comprehensive Treatment of q-Calculus by : Thomas Ernst

Download or read book A Comprehensive Treatment of q-Calculus written by Thomas Ernst and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.

Probabilistic and Analytical Aspects of the Umbral Calculus

Author : Alessandro Di Bucchianico
Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Probabilistic and Analytical Aspects of the Umbral Calculus by : Alessandro Di Bucchianico

Download or read book Probabilistic and Analytical Aspects of the Umbral Calculus written by Alessandro Di Bucchianico and published by . This book was released on 1997 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinatorics: The Rota Way

Author : Joseph P. S. Kung
Publisher : Cambridge University Press
ISBN 13 : 1139476769
Total Pages : 397 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Combinatorics: The Rota Way by : Joseph P. S. Kung

Download or read book Combinatorics: The Rota Way written by Joseph P. S. Kung and published by Cambridge University Press. This book was released on 2009-02-09 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.

A Comprehensive Treatment of q-Calculus

Author : Thomas Ernst
Publisher : Springer Science & Business Media
ISBN 13 : 3034804318
Total Pages : 491 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis A Comprehensive Treatment of q-Calculus by : Thomas Ernst

Download or read book A Comprehensive Treatment of q-Calculus written by Thomas Ernst and published by Springer Science & Business Media. This book was released on 2012-09-13 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.

From Combinatorics to Philosophy

Author : Ernesto Damiani
Publisher : Springer Science & Business Media
ISBN 13 : 0387887539
Total Pages : 267 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis From Combinatorics to Philosophy by : Ernesto Damiani

Download or read book From Combinatorics to Philosophy written by Ernesto Damiani and published by Springer Science & Business Media. This book was released on 2009-07-24 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Combinatorics to Philosophy: The Legacy of G. -C. Rota provides an assessment of G. -C. Rota's legacy to current international research issues in mathematics, philosophy and computer science. This volume includes chapters by leading researchers, as well as a number of invited research papers. Rota’s legacy connects European and Italian research communities to the USA by providing inspiration to several generations of researchers in combinatorics, philosophy and computer science. From Combinatorics to Philosophy: The Legacy of G. -C. Rota is of valuable interest to research institutions and university libraries worldwide. This book is also designed for advanced-level students in mathematics, computer science, and philosophy.

Advances in Combinatorial Methods and Applications to Probability and Statistics

Author : N. Balakrishnan
Publisher : Springer Science & Business Media
ISBN 13 : 1461241405
Total Pages : 576 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Advances in Combinatorial Methods and Applications to Probability and Statistics by : N. Balakrishnan

Download or read book Advances in Combinatorial Methods and Applications to Probability and Statistics written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.

The Search for E. T. Bell

Author : Constance Reid
Publisher : Cambridge University Press
ISBN 13 : 9780883855089
Total Pages : 388 pages
Book Rating : 4.8/5 (55 download)

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Book Synopsis The Search for E. T. Bell by : Constance Reid

Download or read book The Search for E. T. Bell written by Constance Reid and published by Cambridge University Press. This book was released on 1993 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a compelling account of this complicated, difficult man.

Finite Operator Calculus

Author : Gian-Carlo Rota
Publisher :
ISBN 13 :
Total Pages : 292 pages
Book Rating : 4.:/5 (296 download)

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Book Synopsis Finite Operator Calculus by : Gian-Carlo Rota

Download or read book Finite Operator Calculus written by Gian-Carlo Rota and published by . This book was released on 1972 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Finite Calculus Associated with Bessel Functions

Author : Frank M. Cholewinski
Publisher : American Mathematical Soc.
ISBN 13 : 0821850830
Total Pages : 136 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Finite Calculus Associated with Bessel Functions by : Frank M. Cholewinski

Download or read book The Finite Calculus Associated with Bessel Functions written by Frank M. Cholewinski and published by American Mathematical Soc.. This book was released on 1988 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although Bessel functions are among the most widely used functions in applied mathematics, this book is essentially the first to present a calculus associated with this class of functions. The author obtains a generalized umbral calculus associated with the Euler operator and its associated Bessel eigenfunctions for each positive value of an index parameter. For one particular value of this parameter, the functions and operators can be associated with the radial parts of $n$-dimensional Euclidean space objects. Some of the results of this book are in part extensions of the work of Rota and his co-workers on the ordinary umbral calculus and binomial enumeration. The author also introduces a wide variety of new polynomial sequences together with their groups and semigroup compositional properties. Generalized Bernoulli, Euler, and Stirling numbers associated with Bessel functions and the corresponding classes of polynomials are also studied. The book is intended for mathematicians and physicists at the research level in special function theory.

Advanced Linear Algebra

Author : Steven Roman
Publisher : Springer Science & Business Media
ISBN 13 : 038727474X
Total Pages : 488 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Advanced Linear Algebra by : Steven Roman

Download or read book Advanced Linear Algebra written by Steven Roman and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra