“According to Abramowitz and Stegun” or arccoth needn't be uncouth

ABSTRACT

This paper addresses the definitions in OpenMath of the elementary functions. The original OpenMath definitions, like most other sources, simply cite [2] as the definition. We show that this is not adequate, and propose precise definitions, and explore the relationships between these definitions.In particular, we introduce the concept of a couth pair of definitions, e.g. of arcsin and arcsinh, and show that the pair arccot and arccoth can be couth.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.1 Expressions and Their Representation
          Subjects: Representations (general and polynomial)

Additional Classification:
  F. Theory of Computation

  G. Mathematics of Computing

General Terms:
Theory, Verification