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Título : Special Functions of Mathematical (Geo-)Physics Tipo de documento: documento electrónico Autores: Willi Freeden ; SpringerLink (Online service) ; Martin Gutting Editorial: Basel : Springer Basel Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Colección: Applied and Numerical Harmonic Analysis Número de páginas: XV, 501 p. 37 illus., 18 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-0348-0563-6 Idioma : Inglés (eng) Palabras clave: Mathematics Geophysics Atmospheric sciences Harmonic analysis Partial differential equations Special functions Mathematical physics Functions Physics Geophysics/Geodesy Differential Equations Abstract Analysis Sciences Clasificación: 51 Matemáticas Resumen: Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises Nota de contenido: 1 Introduction: Geomathematical Motivation -- Part I: Auxiliary Functions -- 2 The Gamma Function -- 3 Orthogonal Polynomials -- Part II: Spherically Oriented Functions.- 4 Scalar Spherical Harmonics in R^3 -- 5 Vectorial Spherical Harmonics in R^3 -- 6 Spherical Harmonics in R^q -- 7 Classical Bessel Functions -- 8 Bessel Functions in R^q -- Part III: Periodically Oriented Functions -- 9 Lattice Functions in R -- 10 Lattice Functions in R^q -- 11 Concluding Remarks -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0563-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32432 Special Functions of Mathematical (Geo-)Physics [documento electrónico] / Willi Freeden ; SpringerLink (Online service) ; Martin Gutting . - Basel : Springer Basel : Imprint: Birkhäuser, 2013 . - XV, 501 p. 37 illus., 18 illus. in color : online resource. - (Applied and Numerical Harmonic Analysis) .
ISBN : 978-3-0348-0563-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Geophysics Atmospheric sciences Harmonic analysis Partial differential equations Special functions Mathematical physics Functions Physics Geophysics/Geodesy Differential Equations Abstract Analysis Sciences Clasificación: 51 Matemáticas Resumen: Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises Nota de contenido: 1 Introduction: Geomathematical Motivation -- Part I: Auxiliary Functions -- 2 The Gamma Function -- 3 Orthogonal Polynomials -- Part II: Spherically Oriented Functions.- 4 Scalar Spherical Harmonics in R^3 -- 5 Vectorial Spherical Harmonics in R^3 -- 6 Spherical Harmonics in R^q -- 7 Classical Bessel Functions -- 8 Bessel Functions in R^q -- Part III: Periodically Oriented Functions -- 9 Lattice Functions in R -- 10 Lattice Functions in R^q -- 11 Concluding Remarks -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0563-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32432 Ejemplares
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Título : Second Order Differential Equations : Special Functions and Their Classification Tipo de documento: documento electrónico Autores: Gerhard Kristensson ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Número de páginas: XII, 219 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7020-6 Idioma : Inglés (eng) Palabras clave: Mathematics Difference equations Functional Functions of complex variables Differential Special functions Ordinary Equations a Complex Variable and Clasificación: 51 Matemáticas Resumen: Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations. The theory is presented in an entirely self-contained way, starting with an introduction of the solution of the second-order differential equations and then focusingon the systematic treatment and classification of these solutions. Each chapter contains a set of problems which help reinforce the theory. Some of the preliminaries are covered in appendices at the end of the book, one of which provides an introduction to Poincaré-Perron theory, and the appendix also contains a new way of analyzing the asymptomatic behavior of solutions of differential equations. This textbook is appropriate for advanced undergraduate and graduate students in Mathematics, Physics, and Engineering interested in Ordinary and Partial Differntial Equations. A solutions manual is available online Nota de contenido: Basic properties of the solutions -- Equations of Fuchsian type -- Equations with one to four regular singular points -- The hypergeometric differential equation -- Legendre functions and related functions -- Confluent hypergeometric functions -- Heun’s differential equation En línea: http://dx.doi.org/10.1007/978-1-4419-7020-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33639 Second Order Differential Equations : Special Functions and Their Classification [documento electrónico] / Gerhard Kristensson ; SpringerLink (Online service) . - New York, NY : Springer New York, 2010 . - XII, 219 p : online resource.
ISBN : 978-1-4419-7020-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Difference equations Functional Functions of complex variables Differential Special functions Ordinary Equations a Complex Variable and Clasificación: 51 Matemáticas Resumen: Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations. The theory is presented in an entirely self-contained way, starting with an introduction of the solution of the second-order differential equations and then focusingon the systematic treatment and classification of these solutions. Each chapter contains a set of problems which help reinforce the theory. Some of the preliminaries are covered in appendices at the end of the book, one of which provides an introduction to Poincaré-Perron theory, and the appendix also contains a new way of analyzing the asymptomatic behavior of solutions of differential equations. This textbook is appropriate for advanced undergraduate and graduate students in Mathematics, Physics, and Engineering interested in Ordinary and Partial Differntial Equations. A solutions manual is available online Nota de contenido: Basic properties of the solutions -- Equations of Fuchsian type -- Equations with one to four regular singular points -- The hypergeometric differential equation -- Legendre functions and related functions -- Confluent hypergeometric functions -- Heun’s differential equation En línea: http://dx.doi.org/10.1007/978-1-4419-7020-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33639 Ejemplares
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Título : Special Topics in the Theory of Piezoelectricity Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Jiashi Yang Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Número de páginas: XII, 329 p. 89 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-89498-0 Idioma : Inglés (eng) Palabras clave: Mathematics Special functions Optics Electrodynamics Mechanics Mechanics, Applied Continuum mechanics Functions and of Materials Theoretical Clasificación: 51 Matemáticas Resumen: Piezoelectricity has been a steadily growing field, with recent advances made by researchers from applied physics, acoustics, materials science, and engineering. This collective work presents a comprehensive treatment of selected advanced topics in the subject. Every chapter is self-contained and written by international experts who elaborate on special topics. Key features include: * Systematic exposition of topics: from a brief summary of the 3-dimensional theory of linear piezoelectricity to selected topics within the linear theory; and the theory of small fields superposed on a finite bias; * Provides a broad overview of piezoelectric (or electroelastic) materials such as single crystals and ceramics that play a key role in this innovative field; examples provided throughout; *Treats new applications to piezoelectric materials and devices in electronics engineering and civil, mechanical, and aerospace engineering structure; * Examines in detail numerical analysis methods to optimize the design of piezoelectric structures and devices. This book is written for an intermediate graduate level and is intended for researchers, mechanical engineers, and applied mathematicians interested in the advances of piezoelectricity and its new applications, and may be used as a supplemental text to a course where piezoelectricity is a focus. Also by Jiashi Yang: An Introduction to the Theory of Piezoelectricity, © 2005 Springer, 978-0-387-23573-8 Nota de contenido: Basic Equations -- Green’s Functions -- Two-Dimensional Static Problems: Stroh Formalism -- Fracture and Crack Mechanics -- Boundary Element Method -- Waves in Strained/Polarized Media -- Fully Dynamic Theory -- Nonlocal and Gradient Effects En línea: http://dx.doi.org/10.1007/978-0-387-89498-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33920 Special Topics in the Theory of Piezoelectricity [documento electrónico] / SpringerLink (Online service) ; Jiashi Yang . - New York, NY : Springer New York, 2009 . - XII, 329 p. 89 illus : online resource.
ISBN : 978-0-387-89498-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Special functions Optics Electrodynamics Mechanics Mechanics, Applied Continuum mechanics Functions and of Materials Theoretical Clasificación: 51 Matemáticas Resumen: Piezoelectricity has been a steadily growing field, with recent advances made by researchers from applied physics, acoustics, materials science, and engineering. This collective work presents a comprehensive treatment of selected advanced topics in the subject. Every chapter is self-contained and written by international experts who elaborate on special topics. Key features include: * Systematic exposition of topics: from a brief summary of the 3-dimensional theory of linear piezoelectricity to selected topics within the linear theory; and the theory of small fields superposed on a finite bias; * Provides a broad overview of piezoelectric (or electroelastic) materials such as single crystals and ceramics that play a key role in this innovative field; examples provided throughout; *Treats new applications to piezoelectric materials and devices in electronics engineering and civil, mechanical, and aerospace engineering structure; * Examines in detail numerical analysis methods to optimize the design of piezoelectric structures and devices. This book is written for an intermediate graduate level and is intended for researchers, mechanical engineers, and applied mathematicians interested in the advances of piezoelectricity and its new applications, and may be used as a supplemental text to a course where piezoelectricity is a focus. Also by Jiashi Yang: An Introduction to the Theory of Piezoelectricity, © 2005 Springer, 978-0-387-23573-8 Nota de contenido: Basic Equations -- Green’s Functions -- Two-Dimensional Static Problems: Stroh Formalism -- Fracture and Crack Mechanics -- Boundary Element Method -- Waves in Strained/Polarized Media -- Fully Dynamic Theory -- Nonlocal and Gradient Effects En línea: http://dx.doi.org/10.1007/978-0-387-89498-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33920 Ejemplares
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Título : Handbook of Continued Fractions for Special Functions Tipo de documento: documento electrónico Autores: Annie Cuyt ; SpringerLink (Online service) ; Vigdis Brevik Petersen ; Brigitte Verdonk ; Haakon Waadeland ; William B. Jones Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2008 Número de páginas: XVI, 431 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-6949-9 Idioma : Inglés (eng) Palabras clave: Mathematics Science Computer science Special functions Engineering Applied mathematics Functions Appl.Mathematics/Computational Methods of Mathematics, general Computing Engineering, Science, Clasificación: 51 Matemáticas Resumen: Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, namely the Handbook of Mathematical Functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website! Nota de contenido: Basic Theory -- Basics -- Continued fraction representation of functions -- Convergence criteria -- Padé approximants -- Moment theory and orthogonal functions -- Numerics -- Continued fraction construction -- Truncation error bounds -- Continued fraction evaluation -- Special Functions -- On tables and graphs -- Mathematical constants -- Elementary functions -- Gamma function and related functions -- Error function and related integrals -- Exponential integrals and related functions -- Hypergeometric functions -- Confluent hypergeometric functions -- Bessel functions -- Probability functions -- Basic hypergeometric functions En línea: http://dx.doi.org/10.1007/978-1-4020-6949-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34291 Handbook of Continued Fractions for Special Functions [documento electrónico] / Annie Cuyt ; SpringerLink (Online service) ; Vigdis Brevik Petersen ; Brigitte Verdonk ; Haakon Waadeland ; William B. Jones . - Dordrecht : Springer Netherlands, 2008 . - XVI, 431 p : online resource.
ISBN : 978-1-4020-6949-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Science Computer science Special functions Engineering Applied mathematics Functions Appl.Mathematics/Computational Methods of Mathematics, general Computing Engineering, Science, Clasificación: 51 Matemáticas Resumen: Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, namely the Handbook of Mathematical Functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website! Nota de contenido: Basic Theory -- Basics -- Continued fraction representation of functions -- Convergence criteria -- Padé approximants -- Moment theory and orthogonal functions -- Numerics -- Continued fraction construction -- Truncation error bounds -- Continued fraction evaluation -- Special Functions -- On tables and graphs -- Mathematical constants -- Elementary functions -- Gamma function and related functions -- Error function and related integrals -- Exponential integrals and related functions -- Hypergeometric functions -- Confluent hypergeometric functions -- Bessel functions -- Probability functions -- Basic hypergeometric functions En línea: http://dx.doi.org/10.1007/978-1-4020-6949-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34291 Ejemplares
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Título : Theory and Applications of Special Functions : A Volume Dedicated to Mizan Rahman Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Mourad E. H. Ismail ; Erik Koelink Editorial: Boston, MA : Springer US Fecha de publicación: 2005 Colección: Developments in Mathematics, ISSN 1389-2177 num. 13 Número de páginas: XII, 491 p Il.: online resource ISBN/ISSN/DL: 978-0-387-24233-0 Idioma : Inglés (eng) Palabras clave: Mathematics Approximation theory Integral transforms Operational calculus Special functions Functions Approximations and Expansions Transforms, Calculus Clasificación: 51 Matemáticas Resumen: This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. Also, it includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject. Audience This book is intended for researchers and graduate students in special functions, algebraic combinatorics, quantum groups, and integrable systems Nota de contenido: Mizan Rahman, His Mathematics and Literary Writings -- On the Completeness of Sets of q-Bessel Functions J?(3)(x; q) -- a-Gaussian Polynomials and Finite Rogers-Ramanujan Identities -- On a Generalized Gamma Convolution Related to the q-Calculus -- Ramanujan and Cranks -- The Saalschütz Chain Reactions and Multiple q-Series Transformations -- Painlevé Equations and Associated Polynomials -- Zeta Functions of Heisenberg Graphs over Finite Rings -- q-Analogues of Some Multivariable Biorthogonal Polynomials -- Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials -- Continuous Hahn Functions as Clebsch-Gordan Coefficients -- New Proofs of Some q-Series Results -- The Little q-Jacobi Functions of Complex Order -- A Second Addition Formula for Continuous q-Ultraspherical Polynomials -- A Bilateral Series Involving Basic Hypergeometric Functions -- The Hilbert Space Asymptotics of a Class of Orthonormal Polynomials on a Bounded Interval -- Abel-Rothe Type Generalizations of Jacobi's Triple Product Identity -- Summable Sums of Hypergeometric Series -- Askey-Wilson Functions and Quantum Groups -- An Analog of the Cauchy-Hadamard Formula for Expansions in q-Polynomials -- Strong Nonnegative Linearization of Orthogonal Polynomials -- Remarks on Some Basic Hypergeometric Series En línea: http://dx.doi.org/10.1007/b104910 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35080 Theory and Applications of Special Functions : A Volume Dedicated to Mizan Rahman [documento electrónico] / SpringerLink (Online service) ; Mourad E. H. Ismail ; Erik Koelink . - Boston, MA : Springer US, 2005 . - XII, 491 p : online resource. - (Developments in Mathematics, ISSN 1389-2177; 13) .
ISBN : 978-0-387-24233-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Approximation theory Integral transforms Operational calculus Special functions Functions Approximations and Expansions Transforms, Calculus Clasificación: 51 Matemáticas Resumen: This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. Also, it includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject. Audience This book is intended for researchers and graduate students in special functions, algebraic combinatorics, quantum groups, and integrable systems Nota de contenido: Mizan Rahman, His Mathematics and Literary Writings -- On the Completeness of Sets of q-Bessel Functions J?(3)(x; q) -- a-Gaussian Polynomials and Finite Rogers-Ramanujan Identities -- On a Generalized Gamma Convolution Related to the q-Calculus -- Ramanujan and Cranks -- The Saalschütz Chain Reactions and Multiple q-Series Transformations -- Painlevé Equations and Associated Polynomials -- Zeta Functions of Heisenberg Graphs over Finite Rings -- q-Analogues of Some Multivariable Biorthogonal Polynomials -- Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials -- Continuous Hahn Functions as Clebsch-Gordan Coefficients -- New Proofs of Some q-Series Results -- The Little q-Jacobi Functions of Complex Order -- A Second Addition Formula for Continuous q-Ultraspherical Polynomials -- A Bilateral Series Involving Basic Hypergeometric Functions -- The Hilbert Space Asymptotics of a Class of Orthonormal Polynomials on a Bounded Interval -- Abel-Rothe Type Generalizations of Jacobi's Triple Product Identity -- Summable Sums of Hypergeometric Series -- Askey-Wilson Functions and Quantum Groups -- An Analog of the Cauchy-Hadamard Formula for Expansions in q-Polynomials -- Strong Nonnegative Linearization of Orthogonal Polynomials -- Remarks on Some Basic Hypergeometric Series En línea: http://dx.doi.org/10.1007/b104910 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35080 Ejemplares
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