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Table Errata Author(s): H. Van Haeringen and L. P. Kok Source: Mathematics of Computation, Vol. 47, No. 176 (Oct., 1986), pp. 767-768 Published by: American Mathematical Society Stable URL: http://www.jstor.org/stable/2008202 Accessed: 19/04/2010 16:56 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=ams. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. American Mathematical Society is collaborating with JSTOR to digitize, preserve and extend access to Mathematics of Computation. http://www.jstor.org TABLE ERRATA 606. -ELDON R. HANSEN, A Table of Series and Products, Prentice-Hall, Englewood Cliffs, N. J., 1985. p. 132: (6.6.102) In the denominator of the summand, replace (1 - c)k by (1 + C)k p. 138: (6.7.37) Add m = 1,2,... p. 142: (6.9.2) For xr, read Xr. pp. 224, 225: The right members of formulas (14.6.1)-(14.6.3), (14.7.1)-(14.7.3) contain indefinite integrals. To obtain the correct integration constant, one may substitute definite integrals on the interval [0, x], thereby renaming the integration variable as x', for example. p. 308: (47.4.8) For C(q)(x), read C2()(x). p. 311: (47.6.11) The third expression on the right side is incorrect; it should read 21 -2qr(2q ) 1 - x qi I + t2 - 2ts cosxcosy 2(q snxiy) q( 2t sin xsin y Another expression for this sum, very similar to the second expression on the right side, is u 2q2F1(q, q; 2q; 4u-2t sin x sin y). p. 324: (48.23.15) For 3, read 3F3. p. 377: (56.8.1) Add the condition x, y, z E (0, 7r). The condition on the second expression on the right side should read: if Ix - yl < z < x + y < g. Cf. formula (46.9.1) on p. 307. p. 506 Add: Bn m) a generalization of the Bernoulli polynomial (6.7.5), (6.7.26). p. 521: ET For 1953, read 1955. FR For FRANICS, read FRANCIS. p. 522: NO For NORLUND, read NORLUND. p. 523: RZ For RYSHIK, read RYZHIK. SZ For SZEGO, read SZEGO. H. VAN HAERINGEN L. P. KOK Department of Mathematics and Informatics Delft University of Technology Delft, The Netherlands Institute for Theoretical Physics P. 0. Box 800 Groningen, The Netherlands 767 768 TABLE ERRATA 607.-I. S. GRADSHTEYN & I. M. RYZHIK, Table of Integrals, Series, and Products, corrected and enlarged edition prepared by A. Jeffrey, Academic Press, New York, 1980. On page 679 the right member of formula 6.541.2 should read (-1) t' c -2{ I( (bc) K( (ac) 1 __b ____ (ac_2)2p nE _ _ (_bc/2)2k 2 \a Jsingv p= 0 p!F(1-v + P) k=O k!F(1 + v + k) for 0 < b < a, Rec > 0, Rev > n - 1, n = 1,2,.... For 0 < a < b, the arguments a and b should be interchanged. The correct formula was derived by using Barnes' integral representation of the Bessel function JV(z), as proposed originally by Watson [1] for evaluating certain integrals. The error of omitting the term beside I,(bc)K,(ac) appears also in formula (11) on p. 49 of [2] and in formula (12) on p. 213 of [3]. It should be noted that when n = 0 the integral is of Hankel's type [1] and is evaluated correctly in formula 6.541.1 herein. G. SOLT Institut de Physique Universit6 de Neuchatel 2000 Neuchatel, Switzerland 1. (1. N. WATSON, A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, Cambridge, 1966, pp. 434-436 and 428-431. 2. A. ERDtLYI, W. MAGNUS, F. OBERHETTINGER & F. G. TRICOMI, Tables of Integral Transforms, vol. 2, McGraw-Hill, New York, 1954. 3. A. P. PRUDNIKOV, Yu. A. BRYCKOV & 0. I. MARICEV, Integrals and Series, "Nauka", Moscow, 1983. (Russian)