The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more. It shows how much of the subject can be traced back to two equations - the hypergeometric equation and confluent hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including connections to approximation theory, continued fractions, and the moment problem, as well as an introduction to new asymptotic methods. There are also chapters on Meijer G-functions and elliptic functions. The final chapter introduces Painleve transcendents, which have been termed the 'special functions of the twenty-first century'.

The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.

Peter Smith has joined forces with skilled consultants to take his piping series to the next level. The Planning Guide to Piping Design covers the entire process of planning a plant model project from conceptual to mechanical completion, and explains where the piping lead falls in the process along with his roles and responsibilities. Piping Engineering Leads (or PEL's) used to only receive on-the-job training to learn the operation of producing a process plant. Over time, more schools and programs have developed a more advanced curriculum for piping engineers and designers. However, younger generations of engineers and designers are growing up with a much more technological view of piping design and are in need of a handbook that will explain the proven methods of planning and monitoring the piping design in step-by-step processes. This handbook will provide mentors in the process piping industries the bridge needed for the upcoming engineer and designer to grasp the requirements of piping supervision in the modern age.

The Planning Guide to Piping Design, Second Edition, covers the entire process of managing and executing project piping designs, from conceptual to mechanical completion, also explaining what roles and responsibilities are required of the piping lead during the process. The book explains proven piping design methods in step-by-step processes that cover the increasing use of new technologies and software. Extended coverage is provided for the piping lead to manage piping design activities, which include supervising, planning, scheduling, evaluating manpower, monitoring progress and communicating the piping design. With newly revised chapters and the addition of a chapter on CAD software, the book provides the mentorship for piping leads, engineers and designers to grasp the requirements of piping supervision in the modern age.

The description for this book, Calculus on Heisenberg Manifolds. (AM-119), will be forthcoming.

This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.

This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener-Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.

A Colonial Southern Bookshelf studies popular books among southern readers in eighteenth-century America. From booksellers' lists and sale catalogs, Richard Beale Davis's study focuses on three key groups of literature: books in law, politics, and history; books on religious topics; and belles lettres. His examination of the colonial southern library suggests many revealing conclusions: persons of many social and economic levels owned and read books; literacy was more widespread than many historians have perceived; the vast majority of the books in southern libraries were published in England and Europe; and colonial newspapers constituted an important influence on cultural tastes. A Colonial Southern Bookshelf takes a historical look at the popular reading lists of the time and what they say about society in eighteenth-century America. The Georgia Open History Library has been made possible in part by a major grant from the National Endowment for the Humanities: Democracy demands wisdom. Any views, findings, conclusions, or recommendations expressed in this collection, do not necessarily represent those of the National Endowment for the Humanities.

A Colonial Southern Bookshelf studies popular books among southern readers in eighteenth-century America. From booksellers' lists and sale catalogs, Richard Beale Davis's study focuses on three key groups of literature: books in law, politics, and history; books on religious topics; and belles lettres. His examination of the colonial southern library suggests many revealing conclusions: persons of many social and economic levels owned and read books; literacy was more widespread than many historians have perceived; the vast majority of the books in southern libraries were published in England and Europe; and colonial newspapers constituted an important influence on cultural tastes. A Colonial Southern Bookshelf takes a historical look at the popular reading lists of the time and what they say about society in eighteenth-century America. The Georgia Open History Library has been made possible in part by a major grant from the National Endowment for the Humanities: Democracy demands wisdom. Any views, findings, conclusions, or recommendations expressed in this collection, do not necessarily represent those of the National Endowment for the Humanities.

BBC adaptation of Robert Louis Stevenson's classic novel. When Captain Billy Bones (Jack Watson) arrives at Daniel Hawkins (Terry Scully)'s inn, the ailing Hawkins is glad to receive some money from the old sailor. It transpires that Bones has in his possession the map to some hidden treasure in the Bahamas, which he entrusts to Daniel's young son, Jim (Ashley Knight). When Bones' former shipmates, led by Long John Silver (Alfred Burke), arrive to claim the map, Jim escapes. With the help of a local doctor and magistrate, he sets sail for the tropics to discover Treasure Island.

Time and Time Again is a story of time travel, deceit, and murder. From Desert Storm to primitive New Mexico, Jon Allen Stanton lives a double life, one of a twentieth-century man and one of a man caught up in a time warp and living in prehistoric times. His life and purpose for living in those ancient times is a compelling adventure set in two different worlds. Revelation after revelation makes this story take many different twists and turns and lead main character Jon Stanton from now back to then.

I am writing this book in hopes that it will inspire you to examine your own life and to ask yourself whether what you are doing is reasonable and fair. Are your actions serving to advance justice or impede it? When I speak of justice, I'm not just referring to a legal system, but I am referring to truthfulness and integrity in life. Much of what I have to say relates to my career in law. The lessons I learned along the way apply to the life we live every day. My life has been devoted to service. Service to my family, to and through my church, and to my country. My intent in writing this story is to reach young people who are beginning careers or are beginning the education they need in order to gain entry into their chosen fields.

From Transactions Of The American Philosophical Society, V45, Part 2, May, 1955. Correspondence With Jefferson And Other Members Of The American Philosophical Society And With Other Prominent Americans.