7.124 bug in series, Maple 6 to Maple 8 (15.10.01)

7.124.1 Michael Rubinstein

Any explanations as to why the former works but the latter doesn’t?

>  linux174$ maple 
>      |\^/|     Maple 6 (IBM INTEL LINUX) 
>  ._|\|   |/|_. Copyright (c) 2000 by Waterloo Maple Inc. 
>   \  MAPLE  /  All rights reserved. Maple is a registered trademark of 
>   <____ ____>  Waterloo Maple Inc. 
>        |       Type ? for help. 
>  > series(1/(1-x),x); 
>                                  2    3    4    5      6 
>                         1 + x + x  + x  + x  + x  + O(x ) 
> 
>  > series(1/(1-x)^1.,x);
 

7.124.2 Dr Francis J. Wright (16.10.01)

Using floating-point exponents is not something I would want to do without very good reason. However, it seems to me that the second expansion is well defined, and indeed Maple (7) seems quite happy to do it in two steps:

subs(alpha=1., series(1/(1-x)^alpha,x)); 
 
                 2                3                4                5 
  1 + 1. x + 1. x  + 1.000000000 x  + 1.000000000 x  + 1.000000000 x 
 
              6 
         + O(x )
 

So I guess it’s a bug (in Maple 7 also). Since series is a builtin function, there is not much more that we mere mortals to do to investigate it.