§17.18 Methods of Computation
The two main methods for computing basic hypergeometric functions are: (1) numerical summation of the defining series
given in §§17.4(i)
; (2) modular transformations.
Method (1) is applicable within the circles of convergence of the defining series
, although it is often cumbersome owing to slowness of convergence and/or severe cancellation.
applies such methods in several
problems; see Andrews et al. (1986)