Relationship to Euler Transform

Shijun Liao ()
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Shijun Liao: Shanghai Jiao Tong University

Chapter Chapter 5 in Homotopy Analysis Method in Nonlinear Differential Equations, 2012, pp 189-221 from Springer

Abstract: Abstract The so-called generalized Taylor series and homotopy-transform are derived in the frame of the homotopy analysis method (HAM). Some related theorems are proved, which reveal in theory the reason why convergence-control parameter provides us a convenient way to guarantee the convergence of the homotopy-series solution. Especially, it is proved that the homotopy-transform logically contains the famous Euler transform that is often used to accelerate convergence of a series or to make a divergent series convergent. All of these provide us a conner-stone for the concept of convergence-control and the great generality of the HAM.

Keywords: Singular Point; Conver Gence; Divergent Series; Maclaurin Series; Auxiliary Linear Operator (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25132-0_5

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DOI: 10.1007/978-3-642-25132-0_5

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