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The Scope of the Power Series Method

Richard Beals
Mathematics Magazine
Vol. 86, No. 1 (February 2013), pp. 56-62
DOI: 10.4169/math.mag.86.1.056
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.86.1.056
Page Count: 7
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The Scope of the Power Series Method
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Abstract

Summary This note examines the application of the power series method to the solution of second order homogeneous linear ODEs, and shows that it works in a straightforward way only under restrictive conditions—in cases that reduce to the hypergeometric equation or the confluent hypergeometric equation. On the other hand, it is noted that these equations account for most “special functions.”

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