\operatorname{arccoth} (x) = -\frac{i}{2}\pi + x + \frac{1}{3} x^{3} + \frac{1}{5} x^{5} + \frac{1}{7} x^{7} + \frac{1}{9} x^{9} + \frac{1}{11} x^{11} + \frac{1}{13} x^{13} + \frac{1}{15} \\ \quad{}\quad{}x^{15} + \operatorname{O} \bigl(x^{16}\bigr)

`&operatorname`(arccoth)(x) = series(-1/2*I*Pi+1*x+1/3*x^3+1/5*x^5+1/7*x^7+1/9*x^9+1/11*x^11+1/13*x^13+1/15*x^15+O(x^16),x,16)