Recent Mathematical Tables

نویسنده

  • K. Hayashi
چکیده

89[D, E].—Project for Computation of Mathematical Tables (A. N. Lowan, technical director). Tables of Circular and Hyperbolic Sines and Cosines for Radian Arguments. Prepared by the Federal Works Agency, Work Projects Administration for the State of New York, conducted under the sponsorship of the National Bureau of Standards. New York, 1940, 1939. xx, 405 p. 20.9X27 cm. Reproduced by a photo offset process. Sold by the U. S. Bureau of Standards, Washington, D. C. $2.00; foreign $5.00. The main part of this volume (p. 1^100) is occupied with a table of the circular and hyperbolic sines and cosines for the range [0.0000 (0.0001) 1.9999; 9D]. Then follow supplementary tables: II (p. 402-403), circular and hyperbolic sines and cosines for the range{0.0(0.1)10.0; 9D]; and III (p. 404-405) a conversion table for radians and degrees, to 6D. The expansions of the functions involved terms of the form U„(x) = x"/nl The values of this function for the key arguments »o=0.01, 0.02, • • ■ were computed to 15D for n=0, 1, 2, • • • p, where p is such that Up(xti) is not greater than one unit in the fifteenth place. The values of U„(x) for all other arguments were computed with the aid of a recurrence formula, successive applications of which involved self-checking. But the other checks applied included comparison of the values of sin x and cos x at intervals of 0.001 with the values given in Van Orstrand's Table, and in the New York Project's Tables of Sines and Cosines for Radian Arguments, computed by an independent method; see RMT 81. The values of the hyperbolic functions were also checked by combining the values of ez and e-* in the New York Project's volume Tables of the Exponential Function e*, for »= [0.0000(0.0001)1,0000; 18D], and [1.000(0.0001)25000; 15D], and -[0.0000(0.0001)2.5000; 18D]. After these tests, the resulting values of the circular and hyperbolic functions were rounded to 9D. The claim that an error in the ninth place does not exceed 0.51 is doubtless well founded. From the fairly representative bibliography given in RMT 81, it may be noted that so far as the circular functions are concerned, an appreciable portion of the present table covers new ground. Among other published tables of the hyperbolic sines and cosines, to 5D or more, and for real values of x, are the following (compare N 7, IV): Thomas Holmes Blakesley (1847-1929), A Table of Hyperbolic Cosines and Sines . . . (Published by the Physical Society of London), London, 1890, 6 p. 15X24 cm. Cosh x and sinh x for x= [0.01 (0.01)4.00; 7D]. Comparison of this table with only the values of the above mentioned Table II showed the following last figure errors in Blakesley: Cosh *—unit errors for a; =1.30, 1.70, 2.10, 2.60, 2.90, 3.40, 3.60, 3.80, 3.90, and two units for » = 3.10, and three units for »=4.00; sinh »—unit errors for »=1.50, 1.60, 1.80, 2.40, 2.60, 2.80, 3.10, 3.20, 3.30, 3.70, and two units for 3.50, 3.60, and 3.90. Johann Otto Wilhelm Ligowski (1821-1893), Tafeln der Hyperbelfunklionen . . . , Berlin, 1890, 16.4X24.6 cm. P. 58-61, 67-79, sinh x and cosh *, for »=[0.00(0.01)2.00; 6D], [2.00(0.01) 8.00; 5D], with differences. Angiolo Forti, Nuove Tavole delle Funzioni Iperboliche . . . , Rome, 1892. 16.4X23.9 cm. Sinh x and cosh x for » = [0.0000(0.0001)2.000(0.0010)2.010; 6D], [2.00(0.01)8.00; S-7SJ. Becker and Van Orstrand note that in these tables there are frequent errors of 1, 2, and 3 units in the last decimal place. G. F. Becker and C. E. Van Orstrand, Smithsonian Mathematical Tables. Hyperbolic Functions, Washington, Smithsonian Institution, 1909; fifth reprint 1942, p. 88-171. 15X22.9 cm. Sinh » and cosh » for »=[0.0000(0.0001)0.1000; 5D], [0.100(0.001)3.000; 5D], [3.00(0.01)6.00; 4D].

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تاریخ انتشار 2010