# bilateral series

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## 4 matching pages

##### 1: 16.4 Argument Unity

##### 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) ${}_{r}{}^{}\psi _{s}^{}$ 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 …