Shanks' convergence acceleration transform, Padé approximants and partitions

George E Andrews, Ian P Goulden, David M Jackson
1986 Journal of combinatorial theory. Series A  
Shanks developed a method for accelerating the convergence of sequences. When applied to classical sequences in number theory, Shanks' transform yields some famous identities of Euler and Gauss. It is shown here that the Pad&. approximants for the little q-Jacobi polynomials can be used to explain and extend Shanks' observations. The combinatorial significance of these results is also discussed. 0 1986 Academic Press, Inc.
doi:10.1016/0097-3165(86)90024-5 fatcat:xhvkyfscgnccpclo3rgslzjnyu