scholarly journals A Tauberian theorem for a generalized power series method

2005 ◽  
Vol 18 (10) ◽  
pp. 1129-1133 ◽  
Author(s):  
Richard F. Patterson ◽  
Pali Sen ◽  
B.E. Rhoades
Keyword(s):  
Power Series ◽  
Tauberian Theorem ◽  
Series Method ◽  
Power Series Method ◽  
Generalized Power Series

An O-Tauberian theorem and a high indices theorem for power series methods of summability

1994 ◽  
Vol 115 (2) ◽  
pp. 365-375 ◽  
Author(s):  
David Borwein ◽  
Werner Kratz
Keyword(s):  
Power Series ◽  
Tauberian Theorem ◽  
Series Method ◽  
Power Series Method ◽  
Power Series Methods

AbstractWe improve known Tauberian results concerning the power series method of summability Jp based on the sequence {pn} by removing the condition that pn be asymptotically logarithmico-exponential. We also prove an entirely new Tauberian result for rapidly decreasing pn.

scholarly journals Symmetry Analysis and Exact Solutions to the Space-Dependent Coefficient PDEs in Finance

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hanze Liu
Keyword(s):  
Power Series ◽  
Exact Solutions ◽  
Variable Coefficients ◽  
Similarity Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Series Method ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Generalized Power Series

The variable-coefficients partial differential equations (vc-PDEs) in finance are investigated by Lie symmetry analysis and the generalized power series method. All of the geometric vector fields of the equations are obtained; the symmetry reductions and exact solutions to the equations are presented, including the exponentiated solutions and the similarity solutions. Furthermore, the exact analytic solutions are provided by the transformation technique and generalized power series method, which has shown that the combination of Lie symmetry analysis and the generalized power series method is a feasible approach to dealing with exact solutions to the variable-coefficients PDEs.

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