Davis H. The Summation of Series 1962

Textbook in PDF format

The edition originally published by The Principia Press of Trinity University, San Antonio, Texas, 1962.
Valuable as both a text and a reference, this concise monograph starts with a consideration of the calculus of finite differences and advances to discussions of the gamma and psi functions and other methods of summation. Subsequent chapters offer a summation of tables and an examination of infinite sums. The treatment concludes with a table of finite sums and helpful indexes.
This volume was written by a prominent mathematician and educator whose interests encompassed the history of mathematics, statistics, modeling in economics, mathematical physics, and other disciplines. The book is suitable for students, researchers, and applied mathematicians in many areas of mathematics, computer science, and engineering.
The purpose of this small volume is to advance the reader’s understanding of the problem of the summation of series. The device used here is to exhibit differences and summations as the analogues of derivatives and integrals in the infinitesimal calculus. Summation formulas are derived as the inverses of differences in the same way that integration formulas are obtained as the inverses of derivatives. The writer thus introduces as his central exhibit a Table of Finite Sums.
Excellent, clear, useful book.
The Calculus Of Finite Differences
The Gamma and Psi Functions
Other Methods of Summation
Summation by Tables
Infinite Sums
Table of Finite Sums
Indexes