bilateral series

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1: 16.4 Argument Unity

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§16.4(v) Bilateral Series

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2: 17.8 Special Cases of ${}_r{}^{}\psi _r^{}$ Functions

… ►These identities are all given in terms of sums and products of basic bilateral hypergeometric series. …

3: 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).

4: 17.4 Basic Hypergeometric Functions

§17.4 Basic Hypergeometric Functions

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§17.4(ii) ${}_r{}^{}\psi _s^{}$ Functions

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§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 …