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Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55)
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The present volume is an outgrowth of a Conference on Mathematical
Tables held at Cambridge, Mass., on September 15-16, 1954, under the
auspices of the National Science Foundation and the Massachusetts Insti-
tute of Technology. The purpose of the meeting was to evaluate the need
for mathematical tables in the light of the availability of large scale com-
puting machines. It was the consensus of opinion that in spite of the
increasing use of the new machines the basic need for tables would continue
Numerical tables of mathematical functions are in continual demand
by scientists and engineers. A greater variety of functions and higher
accuracy of tabulation are now required as a result of scientific advances
and, especially, of the increasing use of automatic computers. In the latter
connection, the tables serve mainly for preliminary surveys of problems
before programming for machine operation. For those without easy access
to machines, such tables are, of course, indispensable.
Consequently, the Conference recognized that there was a pressing
need for a modernized version of the classical tables of functions of
Jahnke-Emde. To implement the project, the National Science Foundation
requested the National Bureau of Standards to prepare such a volume and
established an Ad Hoc Advisory Committee, with Professor Philip M.
Morse of the Massachusetts Institute of Technology as chairmm, to advise
the staff of the National Bureau of Standards during the course of its
preparation. In addition to the Chairman, the Committee consisted of A.
Erdelyi, M. C. Gray, N. Metropolis, J. B. Rosser, H. C. Thacher, Jr., John
Todd, C. B. Tompkins, and J. W. Tukey.
The primary aim has been to include a maximum of useful informa-
tion within the limits of a moderately large volume, with particular atten-
tion to the needs of scientists in all fields. An attempt has been made to
cover the entire field of special functions. To carry out the goal set forth
by the Ad Hoc Committee, it has been necessary to supplement the tables
by including the mathematical properties that are important in compu-
tation work, as well as by providing numerical methods which demonstrate
the use and extension of the tables.
The Handbook was prepared under the direction of the late Milton
Abramowitz, and Irene A. Stegun. Its success has depended greatly upon
the cooperation of many mathematicians. Their efforts together with the
cooperation of the Ad Hoc Committee are greatly appreciated. The par-
ticular contributions of these and other individuals are acknowledged at
appropriate places in the text. The sponsorship of the National Science
Foundation for the preparation of the material is gratefully recognized.
It is hoped that this volume will not only meet the needs of all table
users but will in many cases acquaint its users with new functions.
ALLEN V. ASTIN, Director
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