Hi Raymond san,
Thanks for looking into this problem. When you create a fix and want to
test it,
drop me the code and I will test it.
Thanks and best regards,
Yasuaki Honda, Chiba, Japan
2012?4?3?0:52 Raymond Toy <toy.raymond at gmail.com>:
>
>
> 2012/4/2 ???? <yasuaki.honda at gmail.com>
>
>> Dear all,
>>
>> It seems that the Maxima function expintegral_ei() behaves unexpectedly
>> for
>> some complex arguments. (There should be some bugs in the implementation).
>>
>> Specifically, considering a line log(20.0)/2+%i*t on the complex plane
>> and t gets
>> increasing, such as t=30, 40, 50.
>> the values can
>> (%i22) expintegral_ei(log(20.0)/2+30*%i);
>> (%o22) 3.116181583331404*%i-.1466880831183789
>>
>> (%i23) expintegral_ei(log(20.0)/2+40*%i);
>> (%o23) 3.205076248461513*%i+.1490949857975915
>>
>> (%i24) expintegral_ei(log(20.0)/2+50*%i);
>> (%o24) 1766.649087960532-1098.205534849491*%i
>>
>> So, (%o24) indicates that somewhere betwee log(20.0)/2+40*%i and
>> log(20.0)/2+50*%i,
>> there is a point where expintegral_ei() starts unstable ( not converge).
>> This function,
>> however, should converge for these values. (See below for the values
>> obtained using
>> mpmath in python).
>>
>> Thanks for reporting this. It looks like it's really an issue with
> expintegral_e. Maxima compute expintegral_ei(z) using expintegral_e(1,-z),
> and the expIntegral_e appears to have problems because it's using a
> series. I think if the continued fraction is used instead, the problem
> goes away.
>
> I'll look into it.
>
> Ray
>
>
>