|
Series values along the real axis Plots of the first terms of the Laurent series of  along the real axis.  labels partial sums up to  . As  increases, the curves vary from red to violet. Because the series misses even terms, the curves for the pairs  and  ,  and  ,  and  coincide. Plots of the first  terms of the Laurent series of  along the real axis for  . As  increases, the curves vary from red to violet. The radius of convergence of the series is π. Series values in the complex plane Curves connecting points  and  by summing successively terms of the Laurent series. The number of terms summed increases from  for the lower plane to  for the upper plane. Zeros of the series in the complex plane Roots of the first  terms of the Laurent series of  in the  . As  increases from 0 to 50, the roots are colored from red to violet and accumulate on a circle of radius  around the origin. Curves of vanishing real part (red) and imaginary part (blue) of the Laurent series of  in the  . Terms up to order  are taken into account. Contour plot of the argument of the Padé approximant  of the function  in the  . The coloring is cyclical from red ( ) to red ( ).
|
