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Integrals Related to the Error Function
Integrals Related to the Error Function presents a table of integrals related to the error function, including indefinite and improper definite integrals. Most of the formulas in this book have not been presented in other tables of integrals or have been presented only for some special cases of parameters or for integration only along the real axis of the complex plane. Many of the integrals presented here cannot be obtained using a computer (except via an approximate numerical integration). Additionally, for improper integrals, this book emphasizes the necessary and sufficient conditions for the validity of the presented formulas, including trajectory for going to infinity on the complex plane; such conditions are usually not given in computer-assisted analytical integration and often not presented in the previously published tables of integrals. Features The first book in English language to present a comprehensive collection of integrals related to the error function Useful for researchers whose work involves the error function (e.g., via probability integrals in communication theory). Additionally, it can also be used by broader audience.
A Method for Computing the Generalized Circular Error Function and the Circular Coverage Function
An efficient method is described for the numerical evaluation by a high speed digital computer of: the integral of an uncorrelated elliptical Gaussian distribution over a circle centered at the mean of the distribution, V(K, c); the integral of a circular Gaussian distribution over a circle offset from the mean of the distribution, P(R, d). The methods are programmed for both the NORC and the IBM 7090. They yield 6 decimal digit accuracy with an average computation time of 10 milliseconds per case on NORC and 6 milliseconds on the 7090. Two extensive inverse tables are included. One gives the radius K as a function V and c, and the other gives the radius R as a function of P and d.
Advanced R
An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.
Calculate the Error of Power Series
This book includes new mathematical forms for calculate error in power series and new form for putting power series for generalized functions and calculate the error for it too.
Professional Excel Development
The definitive guide to developing applications with Microsoft Excel, this book is written by four authors who are Excel MVPs and run their own companies developing Excel-based applications.
