Table of Integrals, Series, and Products [antikvár]

Preface to the Fifth Edition This completely reset fifth edition of Gradshteyn and Ryzhik is a corrected and expanded version of the previous English language edition based on a translation of the fourth Russian edition. The decision to reset the entire book was taken by Academic Press in order to overcome the limitations of the original Russian typesetting that was reproduced photographically in the previous edition, and also to allow many new entries and sections to be added. The larger format now used has enabled most entries to be displayed on a single line, with the consequent result that despite the expansion of the material the number of extra pages required is small. To preserve compatibility with the previous edition, the original numbering system for entries has been retained. New entries and sections have been inserted in a manner consistent with the original scheme. An asterisk following an entiy number indicates either that it is new, or that it has been amended during the preparation of this fifth edition. When an entire section is new, the asterisk has only been added to the section heading. The resetting of the book has made it possible to incorporate not only new corrections, but also addenda contributed by users of the earlier edition together with selected results from related reference works. Whenever possible, new entries and corrections have been checked by means of symbolic computation. The diverse ways in which corrections have been contributed has made it impossible to attribute them to reference sources that are accessible to users of this book. However, as in the previous edition, my indebtedness to these contributors is shown in the form of an acknowledgement list at the front of the book. This list gives the names of those who have written to me directly sending corrections and suggestions for addenda, and added to it are the names of those who have published errata in Mathematics of Computation. I must single out for special thanks Professors H. van Haeringen and L. P. Kok of The Netherlands who over the years have sent me so much material. From amongst the new material included in this fifth edition I would draw attention to some enlargement of the material on orthogonal polynomials, the inclusion of many results relating to theta functions, extra material on other special functions, the greatly enlarged and revised tables of Laplace and Fourier transform pairs and the inclusion of a short table of Mellin transform pairs. The justification for providing these separate tables, some of whose entries can be found elsewhere in the book, is the ease with which the more commonly occurring transform pairs can now be identified. Some additions have been made to the bibliographic references used during the preparation of xix