Hi Raymond san,
Thanks for your comments. I will commit expintegral.lisp and
rtest_expintegral.mac with mentioned changes.
Thanks and best regards,
Yasuaki Honda, Chiba, Japan
2012/04/19 3:04 "Raymond Toy" <toy.raymond at gmail.com>:
>
>
>
> 2012/4/18 ???? <yasuaki.honda at gmail.com>
>>
>> Hi Ray san,
>>
>>
>> > Why the discontinuity on the imaginary axis? Why a radius of 2? Does
this improve accuracy?
>>>>
>>>> There is a point between the radius 1 and 2 simicircles in left half
plane where continued fraction expansion does not converge. So, I picked up
a larger radius. I have not investigated the cf-expansion's convergence
region in detail.
>>>
>>> Do you have an example where the continued fraction does not converge?
I looked at A&S 5.1.22 for the continued fraction and it says it converges
for |arg(z)|<pi, it seems that we could just use the fraction for |z| > 1
and |arg(z)| < .9*pi.
>>
>>
>> That was my original thought, too. However,
expintegral_e(1,-1.700598-0.612828*%i); will not converge if you use
continued fraction expansion. Here is the error message:
>> (%i7) expintegral_e(1,-1.700598-0.612828*%i);
>>
>> expintegral_e: continued fractions failed.#C(-1.700598 -0.612828)
>> -- an error. To debug this try: debugmode(true);
>>
>> Note that abs(-1.700598-0.612828*%i) is around 1.8 .
>
>
> And that the phase is just less than .9*pi so we would apply the
continued fraction.
>
> It would be useful to add this case to the tests, in case someone forgets
why the left and right half-planes have different regions.
>
> I'm quite happy with your patch so feel free to apply it whenever you
want.
>
> Thanks for being so patient and answering my questions.
>
> Ray
>