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Re: Can't calculate numerical derivative of EllipticTheta

• To: mathgroup at smc.vnet.net
• Subject: [mg82677] Re: Can't calculate numerical derivative of EllipticTheta
• From: roland franzius <roland.franzius at uos.de>
• Date: Sun, 28 Oct 2007 04:01:47 -0500 (EST)
• Organization: Universitaet Hannover
• References: <ffv34q$bbm$1@smc.vnet.net>

Scott Hemphill wrote:
> I realize that my version of Mathematica is getting a little old.  Is
> this fixed in later releases?
> 
> In[1]:= $Version
> 
> Out[1]= 5.1 for Linux (October 25, 2004)
> 
> In[2]:= pdf[x_,x0_,sig_] := 1/(Sqrt[2Pi]sig) Exp[-(x-x0)^2/(2sig^2)];
> 
> In[3]:= Sum[pdf[x,0,sig],{x,-Infinity,Infinity}]
> 
>                                       2
>                              -1/(2 sig )
>         EllipticTheta[3, 0, E           ]
> Out[3]= ---------------------------------
>                  Sqrt[2 Pi] sig
> 
> In[4]:= f[sig_]=%;
> 
> In[5]:= f'[1.]
> 
>                                     (0,0,1)
> Out[5]= -1. + 0.241971 EllipticTheta       [3, 0, 0.606531]
> 
> I expected to see a number on this last line.


As far as I see in vs 6.01 the numerical part of elliptic functions and 
the differentiation wrt the index for many other indexed families of 
functions is not implemented too far.

In this case the result is a fourier series

http://functions.wolfram.com/EllipticFunctions/EllipticTheta3/20/01/02/

-- 

Roland Franzius