A Course of Modern Analysis

  title={A Course of Modern Analysis},
  author={Edmund Taylor Whittaker and George Neville Watson},
THE treatise now under notice, which appears as a second edition of a former treatise by one of the authors, is in all essential respects a new work. Its scope has been extended in many directions, and very recent developments, of which a substantial number are due to the authors, receive a fair share of attention. The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner. An unusually complete set of references is… 

5 Functions of a CODlplex Variable

This chapter summarizes the rudiments of complex analysis, which often provides major results with little calculation, and the frequency with which it is resorted to is a testimony to its utility.

The Lambert function, the quintic equation and the proactive discovery of the Implicit Function Theorem

One of the problems on which a great deal of focus is being placed today, is how to teach Calculus in the presence of the massive diffusion of Computer Algebra tools and online resources among

Zero estimates on group varieties II

'The aim of this article is to give an account of a class of estimates that have in recent years been found useful in the theory of transcendental numbers. As our space is limited, and the estimates

TECHNICAL NOTES AND SHORT PAPERS A Method for the Numerical Evaluation of Certain Infinite Integrals

The solution of many physical problems often necessitates the numerical evaluation of infinite real integrals, a common example being that of solutions obtained with the aid of integral transforms.

The period matrices and theta functions of Riemann

This article deals with four notions due to Riemann: (A) Riemann bilinear relations, (B) Riemann forms, (C) Riemann theta functions and (D) Riemann’s theta formula, in four parts. Following the

A Method for Increasing the Efficiency of Monte Carlo Integration

This paper develops a correlated stratified sampling technique whose efficiency generally exceeds that of crude sampling by a factor n 3, n being the number of correlated ('antithetic') variates taken.

In Quest of Bernstein Inequalities Rational Functions, Askey-Wilson Operator, and Summation Identities for Entire Functions

The title of the dissertation gives an indication of the material involved with the connecting thread throughout being the classical Bernstein inequality (and its variants), which provides an

Asymptotic analysis: Working Note No. 2, Approximation of integrals

In this note we discuss the approximation of integrals that depend on a parameter. The basic tool is simple, namely, integration by parts. Of course, the power of the tool is evidenced in

Notes on the central forcern

In this article we collect several results related to the classical problem of two-dimensional motion of a particle in the field of a central force proportional to a real power of the distancer. At