Integrals and Mathematical Formulas
Pocket Book of
Integrals and Mathematical Formulas
Ronald J. Tallarida
Temple University Philadelphia, Pennsylvania, U.S.A.
Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487‑2742 © 2008 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprintof Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid‑free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number‑13: 978‑1‑4200‑6304‑2 (Softcover) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information,but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The Authors and Publishers have attempted to trace the copyright holders of all material reproduced in this publi‑ cation and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledgedplease write and let us know so we may rectify in any future reprint Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without writtenpermission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978‑750‑8400. CCC is a not‑for‑profit organization that provides licenses and registration for a variety of users. For organizations thathave been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Tallarida, Ronald J. Pocket book of integrals and mathematical formulas / author,Ronald J. Tallarida. ‑‑ 4th ed. p. cm. Includes bibliographical references and index. ISBN 978‑1‑4200‑6304‑2 (alk. paper) 1. Integrals‑‑Tables. 2. Mathematics‑‑Tables. I. Title. QA310.T35 2008 510.2’12‑‑dc22 2007045335
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Preface to the Fourth Edition
As in the previousworks, this new edition preserves the content, size, and convenience of this portable reference source for students and workers who use mathematics, while introducing much new material. New in this fourth edition is an expanded chapter on series that now includes many fascinating properties of the natural numbers that follow from number theory, a field that has attracted much new interest since therecent proof of Fermat’s last theorem. While the proofs of many of these theorems are deep, and in some cases still lacking, all the number theory topics included here are easy to describe and form a bridge between arithmetic and higher mathematics. The fourth edition also includes new applications such as the geostationary satellite orbit, drug kinetics (as an application of differentialequations), and an expanded statistics section that now discusses the normal approximation of the binomial distribution as well as a treatment of nonlinear regression. The widespread use of computers now makes the latter topic amenable to all students, and thus all users of the Pocket Book of Integrals can benefit from the concise summary of this topic. The chapter on financial mathematics, introduced...