Mathematical tables

Adapted by permission from Burington, Handbook of Mathematical Tables and Formulas, 3d. ed., McGraw-Hill Book Company, New York (1959). 

M. Abramowitz, I. A. Stegun, eds. Handbook of Mathematical Eunctions with Eormulas, Graphs, and Mathematical Tables. Vol. 55 of National Bureau of Standards Applied Mathematics Series, 9th ed. Washington, DC US Government Printing Office, 1970, pp. 883-884. 

Abramowitz, Milton and Stegun, Irene A. (eds.) Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, U.S. Government Printing Office, Washington, D.C. (1964). 

Abamowitz, M., Stegun, I.A., editors. (1965). Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables. Dover Publications, New York. Bang-Jensen, J., Gutin, G. (2002). Digraphs Theory, Algorithms and Applications. Springer, New York. 

The error function is tabulated in most handbooks of mathematical tables. It is useful to note that erf( —x) = — erf(x) and that... 

Hall/CRC, New York (2004) Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, 2d ed., CRC Press, New York (2002) Wrede, R. C., and Murray R. Spiegel, Schaum s Outline of Theory and Problems of Advanced Calculus, 2d ed., McGraw-Hill, New York (2006) Zwillinger, D., CRC Standard Mathematical Tables and Formulae, 1st ed., CRC Press, New York (2002) http // eqworld.ipmnet.ru/. 

These functions which arise in the way described have been tabulated in Tables of Spherical Bessel Functions 2 vols. (Columbia Univ. Press, 1947) prepared by the Mathematical Tables Project of the National Bureau of Standards. 

Another method is simply to look up the function in mathematics tables. 

In this publication, besides repeating exactly arguments presented earlier in the 1911 article published by his Theosophist co-religionist, which he carefully cites, Noircarme presents us with a mathematical table containing all the constituent elements of an n-dimensional solid. Of particular interest to this student of esoteric geometries was the development of the binomial... 

British Association for the Advancement of Science, 1952. Mathematical Tables, Vol. X Bessel Functions, Part II Functions of Positive Integer Order, Cambridge University Press, Cambridge. 

This is called a point-spread function, because it describes how what should be a point focus by geometrical optics is spread out by diffraction. The expression in the curly brackets is the one that is of interest. The other terms are phase and overall amplitude terms, as are usual with Fraunhofer diffraction expressions. The function Ji is a Bessel function of the first kind of order one, whose values can be looked up in mathematical tables. 2Ji(x)/x, the function in the curly brackets, is known as jinc(x). It is the axially symmetric equivalent of the more familiar sinc(x) = sin(x)/x (Hecht 2002), the diffraction pattern of a single slit, usually plotted in its squared form to represent intensity. Just as sinc(x) has a large central maximum, and then a series of zeros, so does jinc(x). Ji(x) = 0, but by L Hospital s rule the value of Ji(x)/x is then the ratio of the gradients, and jinc(0) = 1. The next zero in Ji(x) occurs when x = 3.832, and so that gives the first zero in jinc(x). This occurs at r = (3.832/n) x (q/2a)Xo in (3.2), which is the origin of the numerical factor in (3.1). 

We first evaluate the discriminant d = (p/3)3 + (q/2)2. If d < 0, then the cubic equation has three (but not necessarily different) real roots. If, on the other hand, d > 0, then the equation has one real root and a conjugate pair of complex roots. Since you find the expressions for the roots in mathematical tables we proceed to the module. 

We have used the same Gauss-Laguerre numerical method to calculate the moments of the data given in Tables I and II. However, scaled s values higher than five were obtained, for which no mathematical tables exist. For narrow distributions with an expected Mw/Mn below 1.3, the method could thus not be used. 

Tables of dav — d /a = y/2t are to be found with most mathematical tables. In Appendix VII we reproduce such a table, where x is the difference dav — d. Note that only one-half of the area under the curve is given in the table. Since the curve is symmetrical, twice the values listed gives the total area. In particular, we should remember that x/

Abramowitz M., Stegun I. A., Handbook of Mathematical Functions with formulas, graphs, and mathematical tables, Dover, New York, 1972. 

Handbook of mathematical functions with formulas, graphs and mathematical tables, edited by M. Abramowitz and I.A. Stegun, (National Bureau of Standards Applied Mathematics... 

MATHEMATICAL TABLES AND FORMULAS, Robert D. Camrichael and Edwin R. Smith. Logarithms, sines, tangents, trig functions, powers, roots, reciprocals, exponential and hyperbolic functions, formulas and theorems. 269pp. 55x854. 60111-0 Pa. 5.95... 

HANDBOOK OF MATHEMATICAL FUNCTIONS WITH FORMULAS. GRAPHS. AND MATHEMATICAL TABLES, edited by Milton Abramowitz and Irene A. Stegun. Vast compendium 29 sets of tables, some to as high as 20 places. 1,046pp. 8 x 105. 61272-4 Pa. 21.95... 

Jannke, E., and F. Emde Tables of functions. New York Dover publication 1945.Voir aussi Mathematical Tables", Vol. I. Ed. British Association for the Advancement of Science. 2nd Edition p. 31—33. Cambridge University Press 1946. 

A2) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. N.B.S. Appl. Math. Ser. 55 (Hrsg. M. Abramowitz und I. A. Stegun). Washington 1965. 

Verdult V (1997) Mathematical tables. Delft University of Technology. http //www.seminaire-sherbrooke.qc.ca/math/Pierre/Tables.pdf. Accessed 19 May 2009... 

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