Abstract
Publisher Summary This chapter describes the connection between Pade approximants and approximations derived from stationary variational principles by considering a particular case, the S-wave scattering of a single particle in nonrelativistic potential theory. It also presents several implications about the convergence of Pade approximant. The chapter shows that a sequence of approximants running parallel to the diagonal of the Pade table may be obtained by restricting the trial function in a variational principle to a particular sequence of finite-demensional subspaces, each one contained in the next. The chapter concludes by proving a new result about the convergence of Pade approximants to a certain class of entire functions. Pade approximants to a certain class of entire functions converge in measure within any given bounded domain of a complex plane.
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