Numerical tables of mathematical functions are in continual demand by scientists and engineers for preliminary surveys of problems before programming for computing machines. This handbook was designed to provide scientific investigators with a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems. The chapters contain numerical tables, graphs, polynomial or rational approximations for automatic computers, and statements of the principal mathematical properties of the tabulated functions. Many numerical examples are given to illustrate the use of the tables and also the computation of function values which lie outside their range. At the end of each chapter is a short list of references in which proofs of the properties may be found and the more important numerical tables. (MNS)