2011 | OriginalPaper | Chapter

# Integral functions

Derive the recurrence relation for the gamma function and evaluate the gamma function for certain rational arguments Evaluate integrals that require the use of the gamma function in their solution Identify the beta function and evaluate integrals that require the use of the beta function in their solution Derive the relationship between the gamma function and the beta function Use the duplication formula to evaluate the gamma function for half integer arguments Recognise the error function and its relation to the Gaussian probability distribution Recognise elliptic functions of the first and second kind Evaluate integrals that require the use of elliptic functions in their solution Use alternative forms of the elliptic functions Solve equations using the Newton-Raphson iterative method Use the modified Newton-Raphson method to find the first approximation when the derivative is small Understand the meaning of interpolation and use simple linear and graphical interpolation Use the Gregory-Newton interpolation formula with forward and backward differences for equally spaced domain points Use the Gauss interpolation formulas using central differences for equally spaced.