Titlebook: Symbolic Asymptotics; John R. Shackell Book 2004 Springer-Verlag Berlin Heidelberg 2004 Computer.Hardy fields.algorithms.asymptotics.compu

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Algebraic Differential Equations,ubstituting a general power series into the equation and then comparing terms in order to find the coefficients. The same idea can be made to work with series in other base functions, and also series where several different base functions may appear, for example . and log . A drawback is that one ha

Certainty

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Implicit Functions,unctions, ..,..., .., the implicit function theorem guarantees the existence of roots .. = ..(.),..., .. = ..(.) of the equations .. = 0,..., .. = 0 in a neighbourhood of any solution point where the rank of the Jacobian matrix is maximal. The root functions .. = .. (.),..., .. = .. (.) are called .

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Oscillating Functions,matical physics, one thing stands out — the absence of trigonometric functions from our theory. Of course, we have seen in Section 5.3 how trigonometric functions composed with functions tending to finite limits can be handled, but these composed functions do not exhibit oscillation. This, the last

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Book 2004 tool. Implementation is beginning to follow...The present book, written by one of the leading specialists in the area, is currently the only one to treat this part of symbolic asymptotics. It contains a good deal of interesting material in a new, developing field of mathematics at the intersection

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Introduction, shall, from time to time, give some consideration to actual implementations. However this book is really about algorithms and the mathematical principles that underlie them, rather than details of implementation.

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Output Data Structures,ether or not this lay behind their reasoning, Abel and Cauchy sought to impose a ban on the use of divergent series. From the point of view of pure mathematics at that time this was undoubtedly justified, but divergent series continued to give surprisingly accurate results, and continued to have their adherents.

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