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# Series for integral of sin^m(ax)cos^n(ax)...? Watch

1. i used to have, in my old formula book, a series formula for this that i discovered after writing out one of these questions (at the time, i didnt know of the reduction formulas).

Unlike reduction formula, this series would allow me to write each term straight down.

So far i have (please dont laugh): (EDIT)

where s= sin, c= cos

for the part, the first term is just:

the second term has in it:

3rd term:

last 3 terms of the mth part are.....3 x 2 x 1

the trouble is, i dont know how to bring this into the series notation thingy - i.e. dont know how to express each term as something to the power of a term in k.

any hints?

thanks for any help/clarity you can give
2. maybe this wont work, as there are 4 different cases for it, which makes it impractical (m odd n even, m even n odd, both even, both odd)
3. (Original post by Hasufel)
i used to have, in my old formula book, a series formula for this that i discovered after writing out one of these questions (at the time, i didnt know of the reduction formulas).

Unlike reduction formula, this series would allow me to write each term straight down.

So far i have (please dont laugh): (EDIT)

where s= sin, c= cos

for the part, the first term is just:

the second term has in it:

3rd term:

last 3 terms of the mth part are.....3 x 2 x 1

the trouble is, i dont know how to bring this into the series notation thingy - i.e. don`t know how to express each term as something to the power of a term in k.

any hints?

thanks for any help/clarity you can give
from k=1 to m-1

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