University of Oxford, 2009. - 123 pages.Contents
Introduction
Background on hypergeometric functions
Relevant properties of hypergeometric functions
Motivation for the computation of hypergeometric functions
Computation of the conuent hypergeometric function 1F1(a; b; z)
Properties of 1F1(a; b; z)
Taylor series
Writing the conuent hypergeometric function as a single fraction
Buchholz polynomials
Asymptotic series
Quadrature methods
Solving the conuent hypergeometric di erential equation
Recurrence relations
Summary and analysis of results
Computation of the Gauss hypergeometric function 2F1(a; b; c; z)
Properties of 2F1
Taylor series
Writing the Gauss hypergeometric function as a single fraction
Quadrature methods
Solving the hypergeometric di erential equation
Transformation formulae
Analytic continuation formulae for z near e i =3
Recurrence relations
Summary and analysis of results
Conclusions, Discussion and Future Considerations
