[Bug-gsl] [bug #33679] gsl_sf_mathieu_se_array calculates zeroth se as non-zero value

[Nikolay Strelkov]

URL:
  <http://savannah.gnu.org/bugs/?33679>

                 Summary: gsl_sf_mathieu_se_array calculates zeroth se as
non-zero value
                 Project: GNU Scientific Library
            Submitted by: nikolays
            Submitted on: Thu 30 Jun 2011 11:20:43 AM GMT
                Category: Runtime error
                Severity: 3 - Normal
        Operating System: Gentoo 10.0 amd64
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: 
         Discussion Lock: Any

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Details:

It is well known, that eigenvalue *b0* for the odd solution b0 is not exist
<http://dlmf.nist.gov/28.2#F1>. Therefore the zeroth odd Mathieu function se
is equal to zero.
In gsl_sf_mathieu_se you have check for trivial case where order=0. But there
is no such check in gsl_sf_mathieu_se_array.

So _gsl_sf_mathieu_se_array_ calculates se0 as non-zero.

I can illustrate my thoughts with simple example (gsl_se_test.c).
It calculates *se* functions for orders 0 and 1 with values of q=-10,0,10. The
program calculates values with _gsl_sf_mathieu_se_ and
_gsl_sf_mathieu_se_array_. As you can see se0 values from array does not equal
to zero:

q = -10.0
        se_0 = 0.0000000000
        se_0 = 0.6115006542 (from array)

q = 10.0
        se_0 = 0.0000000000
        se_0 = 0.6115006542 (from array)

P.S. I use GSL 1.15.



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File Attachments:


-------------------------------------------------------
Date: Thu 30 Jun 2011 11:20:43 AM GMT  Name: gsl_se_test.c  Size: 865B   By:
nikolays
gsl_sf_mathieu_se_array and gsl_sf_mathieu_se test program
<http://savannah.gnu.org/bugs/download.php?file_id=23592>

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