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I know the following recurrence relation

$$a_n=\frac{a+na_{n-1}}{a-n}$$

with $a_0=1$ can be represented alternatively as an integral

$$a_n=a\int_0^1{x^{a-n-1}(2-x)^ndx}$$

Verifying this is easy, but is there any general technique to do this kind of transformations?

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    Do you have a specific "class" or recurrence relations in mind? Otherwise the answer might be "No".2012-03-05
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    @Aryabhata: What conclusions can you draw in general? Even for $$a_n=a\int_0^1{x^{a-n-1}(b-cx)^ndx}$$?2012-03-05
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    I don't understand. Are you looking for general techniques which take you from a recurrence relation to integral, or are you asking if getting an integral representation is any useful?2012-03-05

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