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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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A bit more context and/or an example would be nice. Also, a quote should go with a reference. – Phira May 11 '12 at 7:47
I would both like to know what "this equation" is and what kind of coefficients your two term recurrence is allowed to have. – Phira May 11 '12 at 7:49
Here is the reference : "Hypergeometric operator series and related partial differential equations", [Bragg,1969] – MAK May 11 '12 at 8:04
Satisfied with my answer? – Did Sep 19 '12 at 18:24

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.

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Thank you very maych – MAK May 11 '12 at 12:46

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