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Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations (Hardcover, 2000 ed.): Werner Balser Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations (Hardcover, 2000 ed.)
Werner Balser
R1,564 Discovery Miles 15 640 Ships in 10 - 15 working days

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.

Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations (Paperback, Softcover reprint of the... Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations (Paperback, Softcover reprint of the original 1st ed. 2000)
Werner Balser
R1,530 Discovery Miles 15 300 Ships in 10 - 15 working days

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.

From Divergent Power Series to Analytic Functions - Theory and Application of Multisummable Power Series (Paperback, 1994 ed.):... From Divergent Power Series to Analytic Functions - Theory and Application of Multisummable Power Series (Paperback, 1994 ed.)
Werner Balser
R898 Discovery Miles 8 980 Ships in 10 - 15 working days

Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

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