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If found that : "Assume further that this equation has e series solution $\sum a_ix^i$ whose coefficients are connected by two term recurrence formula. Then, such a series can be expressed in terms of hypergeometric series." [Bragg, 1969]

how can we do this conversion?

thanks in advance

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    Satisfied with my answer?2012-09-19

1 Answers 1

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The (freely downloadable) book A = B, by Petkovsek, Wilf, and Zeilberger, is, generally speaking, a must-read. The authors explain, in particular how to deduce a hypergeometric series from a recurrence relation and the other way round.