How do you find the power series representation for the function #f(x)=sin(x^2)# ? Calculus Power Series Power Series Representations of Functions 1 Answer Wataru 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)!}# Answer link Related questions How do you find the power series representation for the function #f(x)=ln(5-x)# ? How do you find the power series representation of a function? How do you find the power series representation for the function #f(x)=cos(2x)# ? How do you find the power series representation for the function #f(x)=e^(x^2)# ? How do you find the power series representation for the function #f(x)=tan^(-1)(x)# ? How do you find the power series representation for the function #f(x)=(1+x)/(1-x)# ? How do you find the power series representation for the function #f(x)=1/(1-x)# ? How do you find the power series representation for the function #f(x)=1/((1+x)^2)# ? How to find the Laurent series about #z=0# and therefore the residue at #z=0# of #f(z) = 1/(z^4... Question #87417 See all questions in Power Series Representations of Functions Impact of this question 9768 views around the world You can reuse this answer Creative Commons License