scholarly journals Multisummability of formal power series solutions of nonlinear meromorphic differential equations

1992 ◽  
Vol 42 (3) ◽  
pp. 517-540 ◽  
Author(s):  
Boele L. J. Braaksma
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Formal Power Series ◽  
Series Solutions ◽  
Power Series Solutions ◽  
Formal Power ◽  
Meromorphic Differential

scholarly journals Solutions of first level of meromorphic differential equations

1982 ◽  
Vol 25 (2) ◽  
pp. 183-207 ◽  
Author(s):  
W. Balser
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Differential Equations ◽  
Formal Power Series ◽  
Convergent Series ◽  
Constant Matrix ◽  
Image Position ◽  
Formal Power ◽  
Meromorphic Differential Equation ◽  
Meromorphic Differential

Let a meromorphic differential equationbe given, where r is an integer, and the series converges for |z| sufficiently large. Then it is well known that (0.1) is formally satisfied by an expressionwhere F( z) is a formal power series in z–1 times an integer power of z, and F( z) has an inverse of the same kind, L is a constant matrix, andis a diagonal matrix of polynomials qj( z) in a root of z, 1≦ j≦ n. If, for example, all the polynomials in Q( z) are equal, then F( z) can be seen to be a convergent series (see Section 1), whereas if not, then generally the coefficients in F( z) grow so rapidly that F( z) diverges for every (finite) z.

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