Special Functions And Their Applications

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Special Functions And Their Applications

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Author : Nikola? Nikolaevich Lebedev
language : en
Publisher: Courier Corporation
Release Date : 1972-01-01

Special Functions And Their Applications written by Nikola? Nikolaevich Lebedev and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-01-01 with Mathematics categories.

The Russian mathematician views the theoretical and practical aspects of special functions and illustrates their significance in problem solving in physics and engineering

Bessel Functions And Their Applications

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Author : B G Korenev
language : en
Publisher: CRC Press
Release Date : 2002-07-25

Bessel Functions And Their Applications written by B G Korenev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-25 with Mathematics categories.

Bessel functions are associated with a wide range of problems in important areas of mathematical physics. Bessel function theory is applied to problems of acoustics, radio physics, hydrodynamics, and atomic and nuclear physics. Bessel Functions and Their Applications consists of two parts. In Part One, the author presents a clear and rigorous intro

Generalized Associated Legendre Functions And Their Applications

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Author : Nina Opanasivna Virchenko
language : en
Publisher: World Scientific
Release Date : 2001

Generalized Associated Legendre Functions And Their Applications written by Nina Opanasivna Virchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions ? Fq, Meijer's G -function, Fox's H -function, etc. Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions. This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, P m, n ? ( z ) and Q m, n ? ( z ), which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions. The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions P m, n ? ( z ) and Q m, n ? ( z ), the classes of dual and triple integral equations associated with the function P m, n -1/2+i? (cha) etc. Contents: A General Information on Legendre Functions; The Generalized Associated Legendre Functions; The Series Representations of the Generalized Associated Legendre Functions; Relations Between Different Solutions of the Generalized Legendre Equation. Wronskians of Linearly Independent Solutions; Relations Between Contiguous Generalized Associated Legendre Functions; Differential Operators Generated by the Generalized Associated Legendre Equation; Asymptotic Formulas for the Generalized Associated Legendre Functions in a Neighborhood of Singular Points; Asymptotic Representations of the Generalized Associated Legendre Functions as the Functions of Parameters; Integral Representations of the Generalized Associated Legendre Functions of the First Kind; Integral Representations of the Generalized Associated Legendre Functions of the Second Kind; Zeros of the Generalized Associated Legendre Functions; Connection of the Generalized Associated Legendre Functions with the Jacobi Functions; and other topics. Readership: Graduate students and researchers in mathematics, physics and engineer

Special Functions

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Author : George E. Andrews
language : en
Publisher: Cambridge University Press
Release Date : 1999

Special Functions written by George E. Andrews and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

Convex Functions And Their Applications

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Author : Constantin P. Niculescu
language : en
Publisher: Springer Nature
Release Date : 2025-03-11

Convex Functions And Their Applications written by Constantin P. Niculescu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-11 with Mathematics categories.

This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years. These additions are essential for grasping the practical applications of convex function theory in solving contemporary real-world problems. To reflect these advancements, the material has been meticulously reorganized, with a greater emphasis on topics relevant to current research. Additionally, great care has been taken to ensure that the text remains accessible to a broad audience, including both students and researchers focused on the application of mathematics. Ideal for undergraduate courses, graduate seminars, or as a comprehensive reference, this book is an indispensable resource for those seeking to understand the extensive potential of convex function theory.

I Function And Its Applications

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Author : Vinod Prakash Saxena
language : en
Publisher: CRC Press
Release Date : 2024-11-21

I Function And Its Applications written by Vinod Prakash Saxena and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-21 with Mathematics categories.

This book presents the essential role of mathematical modelling and computational methods in representing physical phenomena mathematically, focusing on the significance of the I-function. Serving as a generalized form of special functions, particularly generalised hypergeometric functions, the I-function emerges from solving dual integral equations, prevalent in scenarios such as mixed boundary problems in potential theory, energy diffusion, and population dynamics. Offers the most recent developments on I-function and their application in mathematical modelling and possible applications to some other research areas Expands the area of special functions that have been developed and applied in a variety of fields, such as combinatory, astronomy, applied mathematics, physics, and engineering Highlights the importance of fundamental results and techniques based on the theory of complex analysis and emphasizes articles devoted to the mathematical aspect and applications Shows the importance of fundamental results and techniques derived from the theory of complex analysis, laying the groundwork for further exploration and potential applications of the I-function in solving complex problems Discusses dual integral equations solving and its crucial role in various physical phenomena, such as potential theory and population dynamics Expanding the field of special functions, I-function and Its Applications serves as a platform for recent theories and applications, offering students, researchers, and scholars of Mathematics insight into advanced mathematical techniques and their practical implications across various fields.

Special Functions And Their Applications

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Author : Nikolaĭ Nikolaevich Lebedev
language : en
Publisher:
Release Date : 1965

Special Functions And Their Applications written by Nikolaĭ Nikolaevich Lebedev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Functions categories.

Current Developments In Solid Mechanics And Their Applications

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Author : Holm Altenbach
language : en
Publisher: Springer Nature
Release Date : 2025-07-07

Current Developments In Solid Mechanics And Their Applications written by Holm Altenbach and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-07 with Science categories.

This book is a collection of articles by eminent scientists from different countries who participated in the traditional international conference “Topical Problems of Continuum Mechanics” held at the Institute of Mechanics of the National Academy of Sciences of Armenia since 2007. The topics of the articles: Coupled Fields in Solids, Composites, Soil Mechanics, Fluid Mechanics, Mechanics of Nano-Systems, Structural Mechanics, Biomechanics, Hydraulics and Hydraulic Facilities, Experimental Mechanics.

Mathematical Methods For Physicists International Student Edition

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Author : George B. Arfken
language : en
Publisher: Elsevier
Release Date : 2005-07-05

Mathematical Methods For Physicists International Student Edition written by George B. Arfken and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-05 with Mathematics categories.

This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition. - Updates the leading graduate-level text in mathematical physics - Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering - Focuses on problem-solving skills and offers a vast array of exercises - Clearly illustrates and proves mathematical relations New in the Sixth Edition: - Updated content throughout, based on users' feedback - More advanced sections, including differential forms and the elegant forms of Maxwell's equations - A new chapter on probability and statistics - More elementary sections have been deleted

Reproducing Kernels And Their Applications

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Author : S. Saitoh
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-04-30

Reproducing Kernels And Their Applications written by S. Saitoh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-30 with Mathematics categories.

The First International Congress of the International Society for Analysis, its Applications and Computations (ISAAC'97) was held at the University of Delaware from 3 to 7 June 1997. As specified in the invitation of the President Professor Robert P. Gilbert of the ISAAC, we organized the session on Reproducing Kerneis and Their Applications. In our session, we presented 24 engaging talks on topics of current interest to the research community. As suggested and organized by Professor Gilbert, we hereby publish its Proceedings. Rather than restricting the papers to Congress participants, we asked the Ieading mathematicians in the field of the theory of reproducing kern eIs to submit papers. However, due to time restrietions and a compulsion to limit the Proceedings a reasonable size, we were unable to obtain a comprehensive treatment of the theory of reproducing kernels. Nevertheless, we hope this Proceedings of the First International Conference on reproducing kerneis will become a significant reference volume. Indeed, we believe that the theory of reproducing kernels will stand out as a fundamental and beautiful contribution in mathematical sciences with a broad array of applications to other areas of mathematics and science. We would like to thank Professor Robert Gilbert for his substantial contri bu tions to the Congress and to our Proceedings. We also express our sincere thanks to the staff of the University of Delaware for their manifold cooperation in organizing the Congress.