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§17.18 Methods of Computation

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►The two main methods for computing basic hypergeometric functions are: (1) numerical summation of the defining

series given in §§

17.4(i) and

17.4(ii); (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.
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►Shanks (1955) applies such methods in several

$q$-

series problems; see

Andrews et al. (1986).