s(x) = ∑ [x^(2n+1)] / [(2n+1)!]
and c(x) = ∑(x^2n) / (2n!)
Find the radii of convergence of these series and show that s'(x) =c(x) and c'(x) = s(x) for all xE R
For every α E R, let hα (x) denote the function:
s(x+α)c(α-x) + s(α-x)c(x+α)
show that hα(x) has constant value s(2α)
Use this result or by another means to show that for all β,γ E R
It is difficult for me to write it out on here because I don't know how to write all the maths properly like everybody else on maths forum because I am new!
but for A) I think I must be going wrong because for both s(x) and c(x) the ratio test is telling me they are both null series and thus they converge for all x. Is this correct?
b) I am unsure how to begin this part, maybe i need to use part a)
any advice would be good as I'm having trouble even really starting this question!