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How do you find the power series representation for the function #f(x)=sin(x^2)# ?

1 Answer

Oct 6, 2014

Since

#sinx=sum_{n=0}^infty(-1)^n{x^{2n+1}}/{(2n+1)!}#,

by replacing #x# by #x^2#,

#Rightarrow f(x)=sum_{n=0}^infty(-1)^n{(x^2)^{2n+1}}/{(2n+1)!}#

#=sum_{n=0}^infty(-1)^n{x^{4n+2}}/{(2n+1)!}#

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