The Classical Theory of Polynomial or Rational Approximations

Abstract

This chapter discusses elementary functions including power of binomials, exponential function, trigonometric and hyperbolic functions, logarithm, and inverse trigonometric and hyperbolic functions. Power of binomials includes power series and series of rational fractions. In exponential function series representation is given, followed by functional relations and series of exponentials. An introduction to trigonometric and hyperbolic function is provided with its basic functional relations and special series, along with a series representation of logarithm. In addition, the chapter also discusses the principal values of the inverse trigonometric functions defined by the inequalities and the relationship between the inverse and the direct trigonometric functions are described, followed by the relationship among the inverse trigonometric functions, the inverse hyperbolic functions, and the logarithm.