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MathGroup Archive 2007

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  • To: mathgroup at smc.vnet.net
  • Subject: [mg75622] question
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Mon, 7 May 2007 05:27:42 -0400 (EDT)

Hi.

I want to show that

x/Pi - (1/2)*x*(StruveH[-1, x] + StruveH[1, x])

is equal to zero.

In[36]:=
Plot[Chop[x/Pi - (1/2)*x*(StruveH[-1, x] + StruveH[1, x])], {x, -2,
2}, Axes -> False, Frame -> True]

with Mathematica.

Simplify, FullSimplify, FunctionExpand fail to do this task. Even
replacing x by specific value does
not yield better results.

In[40]:=
FullSimplify[3/Pi - (1/2)*3*(StruveH[-1, 3] + StruveH[1, 3])]

Out[40]=
3/Pi - (3/2)*(StruveH[-1, 3] + StruveH[1, 3])

On the contrary, in another CAS I took

  simplify(3/Pi - (1/2)*3*(StruveH(-1, 3) + StruveH(1, 3)));
  0

Any ideas?

A quick way to show that x/Pi - (1/2)*x*(StruveH[-1, x] + StruveH[1,
x]) is indeed
zero is

In[41]:=
Integrate[x/Pi - (1/2)*x*(StruveH[-1, x] + StruveH[1, x]), x]

Out[41]=
0

but I would really appreciate any other suggestions.

Thanks



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