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Shanks’ transformation

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1: 3.9 Acceleration of Convergence
§3.9(iv) ShanksTransformation
Shankstransformation is a generalization of Aitken’s Δ 2 -process. …
Table 3.9.1: Shankstransformation for s n = j = 1 n ( - 1 ) j + 1 j - 2 .
n t n , 2 t n , 4 t n , 6 t n , 8 t n , 10
2: Bibliography
  • G. E. Andrews, I. P. Goulden, and D. M. Jackson (1986) Shanks’ convergence acceleration transform, Padé approximants and partitions. J. Combin. Theory Ser. A 43 (1), pp. 70–84.
  • 3: Bibliography S
  • D. Shanks (1955) Non-linear transformations of divergent and slowly convergent sequences. J. Math. Phys. 34, pp. 1–42.
  • 4: 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. … Shanks (1955) applies such methods in several q -series problems; see Andrews et al. (1986).