1. The problem statement, all variables and given/known data I need to expand 1/y(x)2 , where y(x)=x1/2Ʃ(-1)n/(n!)2 * (3x/4)n for n=0 to ∞ 2. Relevant equations How does one arrive at the correct solution (-coefficients seem to vanish, only + remain)? 3. The attempt at a solution I know that x1/2Ʃ(-1)n/(n!)2 * (3x/4)n expands to x1/2(1-3/4x+9/64x2-3/256x3...) also, I can follow the expansion of y(x)2 in that it expands to: x(1-3/2x+27/32x2-15/64x3+153/4096x4-27/8192x5+9/65536x6...) or at least Wolfram Alpha can lead me to this expansion which matches the answer. However, I'm stuck at seeing how 1/y(x)2 can expand to: x-1(1+3/2x-27/32x2+15/64x3+...+9/4x2-81/32+...+27/8x3+...) =x-1(1+3/2x+45/32x2+69/64x3+...) It seems to me that there should be some semblance of 1/y(x)2 to y(x)2, and therefore have the +/- coefficients. Wolfram Alpha doesn't seem to be able (willing?) to expand this expression either. Anyone have any tricks for calculating the inverse squared summation? Thanks in advance!