[Scipy-tickets] [SciPy] #1298: Orthogonal polynomials return infinity when evaluated at -1

SciPy Trac scipy-tickets@scipy....
Fri Nov 26 21:50:24 CST 2010


#1298: Orthogonal polynomials return infinity when evaluated at -1
---------------------------+------------------------------------------------
 Reporter:  joelphillips   |       Owner:  pv   
     Type:  defect         |      Status:  new  
 Priority:  high           |   Milestone:  0.9.0
Component:  scipy.special  |     Version:  0.8.0
 Keywords:                 |  
---------------------------+------------------------------------------------

Old description:

> In scipy.special.orthogonal, legendre and jacobi both return infinity
> when evaluated at -1 for all orders greater than or equal to 1.  This is
> incorrect!
>
> Problem only seems to exist at -1.
>
> Example below:
>
> smmc8:~ joel$
> /Library/Frameworks/Python.framework/Versions/2.7/bin/ipython
> Python 2.7 (r27:82508, Jul  3 2010, 21:12:11)
> Type "copyright", "credits" or "license" for more information.
>
> IPython 0.10 -- An enhanced Interactive Python.
> ?         -> Introduction and overview of IPython's features.
> %quickref -> Quick reference.
> help      -> Python's own help system.
> object?   -> Details about 'object'. ?object also works, ?? prints more.
>
> In [1]: import scipy
>
> In [2]: scipy.version.version
> Out[2]: '0.8.0'
>
> In [3]: import scipy.special.orthogonal as sso
>
> In [4]: sso.legendre(1)(-1)
> Out[4]: inf
>
> In [5]: sso.jacobi(3,4,5)(-1)
> Out[5]: inf
>
> In [6]: sso.legendre(1)(-0.999999)
> Out[7]: -0.99999899999999986

New description:

 In scipy.special.orthogonal, legendre and jacobi both return infinity when
 evaluated at -1 for all orders greater than or equal to 1.  This is
 incorrect!

 Problem only seems to exist at -1.

 Example below:
 {{{
 smmc8:~ joel$
 /Library/Frameworks/Python.framework/Versions/2.7/bin/ipython
 Python 2.7 (r27:82508, Jul  3 2010, 21:12:11)
 Type "copyright", "credits" or "license" for more information.

 IPython 0.10 -- An enhanced Interactive Python.
 ?         -> Introduction and overview of IPython's features.
 %quickref -> Quick reference.
 help      -> Python's own help system.
 object?   -> Details about 'object'. ?object also works, ?? prints more.

 In [1]: import scipy

 In [2]: scipy.version.version
 Out[2]: '0.8.0'

 In [3]: import scipy.special.orthogonal as sso

 In [4]: sso.legendre(1)(-1)
 Out[4]: inf

 In [5]: sso.jacobi(3,4,5)(-1)
 Out[5]: inf

 In [6]: sso.legendre(1)(-0.999999)
 Out[7]: -0.99999899999999986
 }}}

--

Comment(by warren.weckesser):

 Add markup to quote the ipython session.

-- 
Ticket URL: <http://projects.scipy.org/scipy/ticket/1298#comment:2>
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