# Populate subscripts in homotopy analysis of equation of motion?

GROUPS:
 Hello, I am seeking to Automate a code by populating subscript k in my equation of Motion. I define phi as a summation being u0+pu1+p^2u2+p^3u3.... and so on. I then define the conditional statement for phi being of value 0 when k is less than or equal to 1 and 1 if k is greater than 1. I then proceed to define the equation of motion for a simple duffing system evaluated with the Homotopy Analysis Method. The governing equation is dependent upon the value of k. k is the order of the Homotopy Analysis Method (HAM). I wanted to tell mathematica to symbolically evaluate the equation for a specific value of k, say 2 or 3. However when i did this the error message "Incomplete expression; more input is needed." came up. Please advise. Thank You HAM Automated Duffing Symbolic Defining Phi \[CurlyTheta] = \!$$\*UnderoverscriptBox[\(\[Sum]$$, $$k = 0$$, $$10$$]$$\(( \(\*SubscriptBox[\(u$$, $$k$$]\)[\[Tau]])\)*$$( \*SuperscriptBox[\(p$$, $$k$$])\)\)\); Defining Chi \[Chi][k_] := If[k <= 1, 0*k, k/k]; Defining HAM Equation for kth Order Subscript[u, k][\[Tau]]'' + \[CapitalOmega]^2* Subscript[u, k][\[Tau]] == \[Chi][ k]*(Subscript[u, k - 1][\[Tau]]'' + \[CapitalOmega]^2* Subscript[u, k - 1][\[Tau]]) + Subscript[c, 0]*(1/(k - 1)!*((\[PartialD]/\[PartialD]\[Tau])((\[PartialD]/\[PartialD]\ \[Tau])(D[\[CurlyTheta], {p, k - 1}] /. p \[RightArrow] 0)) + 2*c*((\[PartialD]/\[PartialD]\[Tau])(D[\[CurlyTheta], {p, k - 1}] /. p \[RightArrow] 0)) + \[Omega]^2*(D[\[CurlyTheta], {p, k - 1}] /. p \[RightArrow] 0) + \[Mu]*(D[\[CurlyTheta]^3, {p, k - 1}] /. p \[RightArrow] 0) - F*(D[Cos[\[CapitalOmega]*\[Tau]], p, k - 1] /. p\[LongRightArrow]0))); % /. {k\[LongRightArrow]1}