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Topic: a rift in the continuum
Replies: 14   Last Post: May 11, 2013 11:32 AM

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Nasser Abbasi

Posts: 5,596
Registered: 2/7/05
Re: a rift in the continuum
Posted: May 9, 2013 2:36 AM
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On 5/8/2013 11:52 PM, clicliclic@freenet.de wrote:
>
> Yesterday I discovered a rift in the continuum of numbers - or perhaps
> just another software bug. In order to make sure I need reliable values
> of the upper incomplete gamma function (that is of the upper-case
> Gamma), namely
>
> Gamma(10^6 + 0.5, 10^6) = ?
>
> and
>
> Gamma(10^6 + 0.5, 1.003*10^6) = ?
>
> to 100 decimal mantissa digits. Independent values (e.g. Maple and MMA)
> would be nice for cross-checking.
>
> Thank you,
>
> Martin.
>


Mathematica V9:
In[230]:= N[Gamma[10^6 + 1/2, 10^6], 100]

Out[230]= \
4.13251479962262062103065157181206841728923017264300442213705199608773\
3766056346603731287344905361003*10^5565705


In[234]:= N[Gamma[10^6 + 1/2, 1003/1000 10^6], 100]
Out[234]= \
1.12717938591210252512349905106484944923179280972477237957652285580320\
7306530531823278504921383679816*10^5565703


Maple 17:
> evalf(GAMMA(10^6+1/2,10^6),100);
0.4132514799622620621030651571812068417289230172643004422137051996087733766\
5565706
056346603731287344905361003 10


evalf(GAMMA(10^6+1/2,1003/1000*10^6),100);
1.12717938591210252512349905106484944923179280972477237957652285\
5565703
5803207306530531823278504921383679652 10


--Nasser




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