Formula for nth derivative of $\arcsin^k(x/2)$

Asked Apr 07 '14 at 13:38

Active Apr 07 '14 at 13:40

Viewed 192 times

I need to find formula for $n$-th derivative of $\arcsin^k(\frac{x}{2})$.

I have found formula for

$$\left(\arcsin\frac{x}{2}\right)^{(n)}=\frac{(-i)^{n-1}(n-1)!}{\left(4-z^2\right)^{n/2}}P_{n-1}\left(\frac{i z}{\sqrt{4-z^2}}\right)$$

Where $P_n$ - Legendre polynomial.

I have found on the net formula for $n$-th derivative of composite function, however it didn't help. How can I find required formula?

edited Apr 07 '14 at 13:40

5xum

asked Apr 07 '14 at 13:38

Somnium

possible duplicate of Nth derivative of $\tan^m x$ – 5xum Apr 07 '14 at 13:40
1

@5xum That page is about $\tan^m x$, as the title claims. I don't see an obvious reduction to $\arcsin^m x$, do you? – Mario Carneiro Apr 07 '14 at 13:57
@5xum Maybe you can explain how to do something similar to $tan^m x$? – Somnium Apr 07 '14 at 20:49

0 Answers0