A Treatise on Bessel Functions: And Their Applications to Physics (Classic Reprint) - Hardcover

Gray, Andrew

9781528160391: A Treatise on Bessel Functions: And Their Applications to Physics (Classic Reprint)

Hardcover

ISBN 10: 1528160398 ISBN 13: 9781528160391

Publisher: Forgotten Books, 2018

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Excerpt from A Treatise on Bessel Functions: And Their Applications to Physics

This book has been written in view of the great and growing importance of the Bessel functions in almost every branch of mathematical physics; and its principal object is to supply in a convenient form so much of the theory of the functions as is necessary for their practical application, and to illustrate their use by a selection of physical problems, worked out in some detail.

Some readers may be inclined to think that the earlier chapters contain a needless amount of tedious analysis; but it must be remembered that the properties of the Bessel functions are not without an interest of their own on purely mathematical grounds, and that they afi'ord excellent illustrations of the more recent theory of differential equations, and of the theory of a complex variable. And even from the purely physical point of View it is impossible to say that an analytical formula is useless for practical purposes; it may be so now, but experience has repeatedly shown that the most abstract analysis may unexpectedly prove to be of the highest importance in mathematical physics. As a matter of fact it will be found that little, if any, of the analytical theory included in the present work has failed to be of some use or other in the later chapters; and we are so far from thinking that anything superﬂuous has been inserted, that we could almost wish that space would have allowed of a more extended treatment, especially in the chapters on the complex theory and on definite integrals.

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