First you problably mean that,Originally Posted bynath_quam

otherwise the function is not defined, which means that ,

makes no sense at all!.

Assuming you mean,

Use integration by parts,

let, then, and, then,

Thus,

Thus,

The trick is to express,

as,

Thus,

Working with the integral we have,

=

Let,

Then, as we have shown,

Which is,

Thus,

Thus,

Thus,

Thus, the recurrence formula is,

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Credits:

I learend the box trick from Soroban