possible bug in symbolic sum of a trig series

• To: mathgroup at smc.vnet.net
• Subject: [mg99343] possible bug in symbolic sum of a trig series
• From: isaac <davidbhatt at gmail.com>
• Date: Sun, 3 May 2009 05:22:17 -0400 (EDT)

```Deal all,
I wrote the following code

In[6]:= ey[y_,n_,L_]:=Cos[n Pi y/L ]
beta[g_,nn_,L_]=(2/L)Integrate[ey[y,nn,L] g[y],{y,0,L}];
beta[g_,0,L_]=(2/L)Integrate[ g[y],{y,0,L}];
In[9]:=  hh[y_]:=y^2
In[15]:= Clear[hha];
hha[y_,mm_]=   With[{L=15},(1/2)beta[hh,0,L]+Sum[beta
[hh,nn,L] ey[y,nn,L],{nn,0,mm}]]// FullSimplify
Out[15]= \!\(\(\(1\/\[Pi]\^2\)\((75\ \[ExponentialE]\^\(\(-\(1\/15\)\)
\ \[ImaginaryI]\ \
\[Pi]\ y\)\ \((6\ \((\(-\[ExponentialE]\^\(\(-\(1\/15\)\)\ \
[ImaginaryI]\ \
\[Pi]\ y\)\))\)\^mm\ LerchPhi[\(-\[ExponentialE]\^\(\(-\(1\/15\)\)\ \
\[ImaginaryI]\ \[Pi]\ y\)\), 2,
1 + mm] + \[ExponentialE]\^\(\(\[ImaginaryI]\ \[Pi]\ y\)
\/15\)\ \
\((2\ \[Pi]\^2 -
6\ \((\(-\[ExponentialE]\^\(\(\[ImaginaryI]\ \[Pi]\ y\)
\/15\)\
\))\)\^\(1 + mm\)\ LerchPhi[\(-\[ExponentialE]\^\(\(\[ImaginaryI]\ \
[Pi]\ y\)\
\/15\)\), 2, 1 + mm] -
3\ Log[\[ExponentialE]\^\(\(-\(1\/15\)\)\ \[ImaginaryI]
\ \
\[Pi]\ y\)]\^2)\))\))\)\)\)
In[17]:= hha[0,100]//N
Out[17]= 150.005
In[19]:= beta[hh,0,15]
Out[19]= 150
(*********why this shift in zero is occuring  it seems it is equal to
zeroth coefficient**********)

The symbolic sum is giving error. I checked with using
FourierTrigSeries and it gave exact answer.

With regards
Isaac
can anybody help?

```

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