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A Treatise On The Theory Of Bessel Functions
Originally published in 1992, this monumental treatise had two major objectives at that time--the development of applications of the fundamental processes of the theory of complex variables and the compiling of a collection of results of value for mathematicians and physicists who encounter Bessel functions.
Hardcover
First published January 3, 1944
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August 16, 2016
If anyone should find himself wandering along a dusty stack and from it takes this book in hand, then "Welcome to British mathematics circa 1900"! And a lot of moderns find it off putting, thank your very much! This book is big and makes use of some things that are obsolete today. It slugs things out and has smell of the notorious Cambridge Tripos (Watson was from Cambridge and Senior Wrangler) about it, yet without being pedantic. But work you must and that's probably why youngsters rank it so low. In those days one did one's mathematics sitting bolt upright, pencil and paper in hand--no radio, no TV, no distractions.
How surprising, then, to learn that it was considered to be state of the art; even breaking from the impenetrability that characterized a lot of 19th century British Mathematics. In fact, according to a review (1924) by one R. D. Carmichael (Carmichael's Theorem, anybody?) it was meant not only to meet the standards of the mathematician but also to be a compendium "include[ing] all formulas, whether general or special, which, although without theoretical interest, are likely to be required in practical applications." Imagine that, a mathematician bowing to the practical needs of outsiders and dutifully recording facts! Boring! (speaks the modern mathematician)
Some would say that this kind of yeomanry was once the strength of mathematics. Back then people solved problems as opposed to constructing masterful generalizations. Physics was less speculative and tied to an experimental tradition that had more in common with working in a machinist's shop than in an academic laboratory--as did the great Henry Ford. The scientist was still a tinker making, from scratch, his own equipment; which even affected the Olympian heights of theory for if one goes back a few decades from when Carmichael's review was written he will find it in Maxwell's famous treatise. As I recall, he included details on the construction of actual machines. (As a smart aleck undergrad I thought such shop talk was beneath me--reminded me of my granddad puttering around in the garage.)
Moreover, being partly a repository for formulas, it has meant that very few have actually "read" this work. I certainly haven't but have on many occasions used it as a compendium and occasionally worked out some of the material adjacent to that of my interest. Another beauty of the book is that one can dip into the various sections without having to read the preceding material. The book doesn't require a lot of rabbit hunting for specialized symbols and to ferret out the author's use of jargon of his making.
As Carmichael points out, some of the general theory for the material in this book is to be found in the masterful Course of Modern Analysis, for which, I believe, there is still a following. Rightly so and, as one who is not a mathematician but enjoys math, I have enjoyed my excursions in this latter work.
As I now enter my retirement years I wonder if I'll have occasion to dip into Bessel functions again? They are surprisingly ubiquitous even appearing in probability theory an statistics. You never know!
How surprising, then, to learn that it was considered to be state of the art; even breaking from the impenetrability that characterized a lot of 19th century British Mathematics. In fact, according to a review (1924) by one R. D. Carmichael (Carmichael's Theorem, anybody?) it was meant not only to meet the standards of the mathematician but also to be a compendium "include[ing] all formulas, whether general or special, which, although without theoretical interest, are likely to be required in practical applications." Imagine that, a mathematician bowing to the practical needs of outsiders and dutifully recording facts! Boring! (speaks the modern mathematician)
Some would say that this kind of yeomanry was once the strength of mathematics. Back then people solved problems as opposed to constructing masterful generalizations. Physics was less speculative and tied to an experimental tradition that had more in common with working in a machinist's shop than in an academic laboratory--as did the great Henry Ford. The scientist was still a tinker making, from scratch, his own equipment; which even affected the Olympian heights of theory for if one goes back a few decades from when Carmichael's review was written he will find it in Maxwell's famous treatise. As I recall, he included details on the construction of actual machines. (As a smart aleck undergrad I thought such shop talk was beneath me--reminded me of my granddad puttering around in the garage.)
Moreover, being partly a repository for formulas, it has meant that very few have actually "read" this work. I certainly haven't but have on many occasions used it as a compendium and occasionally worked out some of the material adjacent to that of my interest. Another beauty of the book is that one can dip into the various sections without having to read the preceding material. The book doesn't require a lot of rabbit hunting for specialized symbols and to ferret out the author's use of jargon of his making.
As Carmichael points out, some of the general theory for the material in this book is to be found in the masterful Course of Modern Analysis, for which, I believe, there is still a following. Rightly so and, as one who is not a mathematician but enjoys math, I have enjoyed my excursions in this latter work.
As I now enter my retirement years I wonder if I'll have occasion to dip into Bessel functions again? They are surprisingly ubiquitous even appearing in probability theory an statistics. You never know!
Displaying 1 of 1 review