Local optimization of the summation of divergent power series

2000 ◽  
Vol 41 (8) ◽  
pp. 5814-5831 ◽  
Author(s):  
J. R. Walkup ◽  
M. Dunn ◽  
D. K. Watson
Keyword(s):  
Power Series ◽  
Local Optimization ◽  
Divergent Power Series

A note on the summation of divergent power series

1969 ◽  
Vol 66 (1) ◽  
pp. 109-114 ◽  
Author(s):  
R. E. Scraton
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Severe Restriction ◽  
Mathematical Problems ◽  
Divergent Power Series ◽  
Euler Transformation ◽  
Direct Use

Many mathematical problems which do not yield a closed-form solution admit of a solution in the form of a power series; differential equations are an obvious example. The direct use of this power series is limited to the interior of its circle of convergence, and this places a restriction—often a severe restriction—on its usefulness. The method described in this paper enables this restriction to be alleviated in many cases; it also enables the convergence of a power series within its circle of convergence to be improved. The method is based on the Euler transformation.

scholarly journals A new method to sum divergent power series: educated match

2017 ◽  
Vol 1 (2) ◽  
pp. 025005 ◽  
Author(s):  
Gabriel Álvarez ◽  
Harris J Silverstone
Keyword(s):  
Power Series ◽  
New Method ◽  
Divergent Power Series

scholarly journals On the summability of divergent power series satisfying singular PDEs

2019 ◽  
Vol 357 (3) ◽  
pp. 258-262 ◽  
Author(s):  
Hua Chen ◽  
Zhuangchu Luo ◽  
Changgui Zhang
Keyword(s):  
Power Series ◽  
Divergent Power Series ◽  
Singular Pdes

On convergence sets of divergent power series

2012 ◽  
Vol 106 ◽  
pp. 193-198
Author(s):  
Buma L. Fridman ◽  
Daowei Ma ◽  
Tejinder S. Neelon
Keyword(s):  
Power Series ◽  
Divergent Power Series
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