Finding the coefficients in fractional order polynomials with maple

Question

I want to find coefficients in fractional order polynomials with Maple software but I'm having trouble. For example, $$ coeff(x+x^{1/2},x,1/2) $$ or $$ coeff(2x^{3/2},x,3/2) $$ Please guide me, Thanks

Answer 1

The reason it doesn't work is that these are, unsurprisingly, not considered to be polynomials. The simplest method to achieve your aim is to do

coeff(MultiSeries:-series(subs(x=u^2,x+x^(1/2)),u),u,1);

and

coeff(MultiSeries:-series(subs(x=u^2,2*x^(3/2)),u),u,3);

where the pattern should be clear.