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bilateral series


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1: 16.4 Argument Unity
§16.4(v) Bilateral Series
2: 17.18 Methods of Computation
§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) 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. … Shanks (1955) applies such methods in several q -series problems; see Andrews et al. (1986).
3: 17.4 Basic Hypergeometric Functions
§17.4 Basic Hypergeometric Functions
§17.4(ii) ψ s r Functions
§17.4(iv) Classification
The series (17.4.1) is said to be balanced or Saalschützian when it terminates, r = s , z = q , and … The series (17.4.1) is said to be k-balanced when r = s and …