Re: approach used in special function iti0k0

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Hi Mark,

The relevant reference is *Computation of Special Functions, Shanjie Zhang
and Jianming Jin, 1996, John Wiley & Sons, Inc.*
See section 6.2., pages 207-212 of the original edition. It seems like it
would be a good idea to add this reference to the
docstring.

Best,
Albert



On Sun, Jun 5, 2022 at 10:08 AM Mark Bakker <[email protected]> wrote:

> I am searching for the approach/algorithm used to compute the special fun=
ction iti0k0. The docs only state that the integrals \int_0^x I_0(t) dt and=
 \int_0^x K_0(t) dt are computed, but I couldn't find a link/reference to t=
he algorithm/approach used to compute these.
>
> Even iti0k0?? doesn't help.
>
>
> Anybody know?
>
>
> Thanks,
>
>
> Mark
>
> _______________________________________________
> SciPy-User mailing list -- [email protected]
> To unsubscribe send an email to [email protected]
> https://mail.python.org/mailman3/lists/scipy-user.python.org/
> Member address: [email protected]
>

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<div dir=3D"ltr"><div>Hi Mark,</div><div><br></div><div>The relevant refere=
nce is <i><span class=3D"gmail-pl-c">Computation of Special Functions, <spa=
n class=3D"gmail-pl-c"> Shanjie Zhang and Jianming Jin, </span>1996, John W=
iley &amp; Sons, Inc.</span></i></div><div><span class=3D"gmail-pl-c">See s=
ection 6.2., pages 207-212 of the original edition. It seems like it would =
be a good idea to add this reference to the</span></div><div><span class=3D=
"gmail-pl-c">docstring.</span></div><div><span class=3D"gmail-pl-c"><br></s=
pan></div><div><span class=3D"gmail-pl-c">Best,</span></div><div><span clas=
s=3D"gmail-pl-c">Albert<br></span></div><div><i><span class=3D"gmail-pl-c">=
</span></i></div><div><table class=3D"gmail-highlight gmail-tab-size gmail-=
js-file-line-container gmail-js-code-nav-container gmail-js-tagsearch-file"=
><tbody><tr><td id=3D"gmail-LC6" class=3D"gmail-blob-code gmail-blob-code-i=
nner gmail-js-file-line"><span class=3D"gmail-pl-c"><br><br></span></td>
        </tr>
        <tr>
          </tr></tbody></table></div></div><br><div class=3D"gmail_quote"><=
div dir=3D"ltr" class=3D"gmail_attr">On Sun, Jun 5, 2022 at 10:08 AM Mark B=
akker &lt;<a href=3D"mailto:[email protected]">[email protected]</a>&gt; wr=
ote:<br></div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px=
 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir=3D=
"ltr"><pre style=3D"box-sizing:unset;border:medium none;margin-top:0px;marg=
in-bottom:0px;padding:0px;overflow:auto;word-break:break-all;white-space:pr=
e-wrap">I am searching for the approach/algorithm used to compute the speci=
al function <span style=3D"font-family:Arial,Helvetica,sans-serif">iti0k0. =
The docs only state that the integrals </span><span style=3D"font-family:Ar=
ial,Helvetica,sans-serif">\int_0^x I_0(t) dt and </span><span style=3D"font=
-family:Arial,Helvetica,sans-serif">\int_0^x K_0(t) dt are computed, but I =
couldn&#39;t find a link/reference to the algorithm/approach used to comput=
e these.=C2=A0</span></pre><pre style=3D"box-sizing:unset;border:medium non=
e;margin-top:0px;margin-bottom:0px;padding:0px;overflow:auto;word-break:bre=
ak-all;white-space:pre-wrap"><span style=3D"font-family:Arial,Helvetica,san=
s-serif">Even </span><span style=3D"font-family:Arial,Helvetica,sans-serif"=
>iti0k0?? doesn&#39;t help.</span></pre><pre style=3D"box-sizing:unset;bord=
er:medium none;margin-top:0px;margin-bottom:0px;padding:0px;overflow:auto;w=
ord-break:break-all;white-space:pre-wrap"><span style=3D"font-family:Arial,=
Helvetica,sans-serif"><br></span></pre><pre style=3D"box-sizing:unset;borde=
r:medium none;margin-top:0px;margin-bottom:0px;padding:0px;overflow:auto;wo=
rd-break:break-all;white-space:pre-wrap"><span style=3D"font-family:Arial,H=
elvetica,sans-serif">Anybody know?</span></pre><pre style=3D"box-sizing:uns=
et;border:medium none;margin-top:0px;margin-bottom:0px;padding:0px;overflow=
:auto;word-break:break-all;white-space:pre-wrap"><span style=3D"font-family=
:Arial,Helvetica,sans-serif"><br></span></pre><pre style=3D"box-sizing:unse=
t;border:medium none;margin-top:0px;margin-bottom:0px;padding:0px;overflow:=
auto;word-break:break-all;white-space:pre-wrap"><span style=3D"font-family:=
Arial,Helvetica,sans-serif">Thanks,</span></pre><pre style=3D"box-sizing:un=
set;border:medium none;margin-top:0px;margin-bottom:0px;padding:0px;overflo=
w:auto;word-break:break-all;white-space:pre-wrap"><span style=3D"font-famil=
y:Arial,Helvetica,sans-serif"><br></span></pre><pre style=3D"box-sizing:uns=
et;border:medium none;margin-top:0px;margin-bottom:0px;padding:0px;overflow=
:auto;word-break:break-all;white-space:pre-wrap"><span style=3D"font-family=
:Arial,Helvetica,sans-serif">Mark</span></pre></div>
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</blockquote></div>

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