On series solutions of $y'' - f(x)y=0$ and applications

dc.contributor.author	Shivakumar, Pappur N
dc.contributor.author	Zhang, Yang
dc.date.accessioned	2013-03-27T08:07:25Z
dc.date.available	2013-03-27T08:07:25Z
dc.date.issued	2013-03-04
dc.date.updated	2013-03-27T08:07:25Z
dc.description.abstract	AbstractIn this paper, we develop explicit expressions for the Taylor series coefficients in the formal Taylor series solution of the second-order linear differential equation y ″ − f ( x ) y = 0 for a given arbitrary function f ( x ) in terms of initial conditions. As applications, we apply our results to f ( x ) = e x , cos ( x ) and Airy’s equation and give explicit formulas for the Taylor coefficients of exp ( ∑ k = 0 ∞ a k x k ) , which is a long-standing question.
dc.description.version	Peer Reviewed
dc.identifier.citation	Advances in Difference Equations. 2013 Mar 04;2013(1):47
dc.identifier.doi	http://dx.doi.org/10.1186/1687-1847-2013-47
dc.identifier.uri	http://hdl.handle.net/1993/18108
dc.language.rfc3066	en
dc.rights	open access	en_US
dc.rights.holder	Pappur N Shivakumar et al.; licensee BioMed Central Ltd.
dc.title	On series solutions of $y'' - f(x)y=0$ and applications
dc.type	Journal Article

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