New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | MEDIUM | LARGE Below is the OCR-scanned text from this page: x INTRODUCTION 3. Auxiliary Functions and Arguments One of the objects of this Handbook is to pro- vide tables or computing methods which enable the user to evaluate the tabulated functions over complele ranges of real values of their parameters. In order to achieve this object, frequent use has been made of auxiliary functions to remove the infinite part of the original functions a t their singularities, and auxiliary arguments to co e with cedure clear. The exponential integral of positive apgument is given by infinite ranges. An example will make t % e pro- x 22 xa =7+lnx+-+-+-+ . . . 1.1! 2:2! 3.3! The logarithmic singularity precludes direct inter- polation near z=O. The functions Ei(x)---In z and cc-’[Ei(z)-ln 2-71, however, are well- behaved and readily interpolable in this region. Either will do as an auxiliary function; the latter was in fact selected as it yields slightly higher accuracy when Ei(z) is recovered. The function P[Ei(z)-ln 2-71 has been tabulated to nine decimals for the range O