- #1
utkarshakash
Gold Member
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- 13
Homework Statement
IF [itex]e^{m \arctan x}=a_0 + a_1x + a_2x^2 + a_3x^3...+a_nx^n+...[/itex]
prove that [itex](n+1)a_{n+1} + (n-1)a_{n-1}=ma_n [/itex]
and hence obtain the expansion of [itex]e^{m \arctan x} [/itex].
Homework Equations
The Attempt at a Solution
$$e^{m \arctan x} = 1+m \arctan x + (m \arctan x)^2/2! + (m \arctan x)^3/3! + ...$$
But I need to simplify this expansion in terms of x and I'm clueless how to do that.