Hi, i want to have a reduction formula for this problem i hope that you can help me with this
J[k] = int((x^2-121)^k, x = 0 .. 11)
thanks in advance
Assuming you're familiar with the hyperbolic functions sinh and cosh, I think the simplest approach (and I leave myself wide open to an *ahem* from someone like Krizalid) is to first make the substitution .
This will lead to which can be done using a well known reduction formula (that you might find easier to derive):
.
Then just sub back ....