From Divergent Power Series to Analytic Functions
Balser, Werner.
From Divergent Power Series to Analytic Functions Theory and Application of Multisummable Power Series / [electronic resource] : by Werner Balser. - X, 114 p. online resource. - Lecture Notes in Mathematics, 1582 0075-8434 ; . - Lecture Notes in Mathematics, 1582 .
Asymptotic power series -- Laplace and borel transforms -- Summable power series -- Cauchy-Heine transform -- Acceleration operators -- Multisummable power series -- Some equivalent definitions of multisummability -- Formal solutions to non-linear ODE.
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.
9783540485940
10.1007/BFb0073564 doi
Functions of complex variables.
Global analysis (Mathematics).
Functions of a Complex Variable.
Analysis.
Theoretical, Mathematical and Computational Physics.
QA331-355
515.9
From Divergent Power Series to Analytic Functions Theory and Application of Multisummable Power Series / [electronic resource] : by Werner Balser. - X, 114 p. online resource. - Lecture Notes in Mathematics, 1582 0075-8434 ; . - Lecture Notes in Mathematics, 1582 .
Asymptotic power series -- Laplace and borel transforms -- Summable power series -- Cauchy-Heine transform -- Acceleration operators -- Multisummable power series -- Some equivalent definitions of multisummability -- Formal solutions to non-linear ODE.
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.
9783540485940
10.1007/BFb0073564 doi
Functions of complex variables.
Global analysis (Mathematics).
Functions of a Complex Variable.
Analysis.
Theoretical, Mathematical and Computational Physics.
QA331-355
515.9