Re: More Laplace of Struve



>>>>> "Raymond" == Raymond Toy  writes:

    Raymond> If I look at hstf in hypgeo.lisp, it seems that it's returning

    Raymond> 2*2^(-v-1)*z^(v+1)/sqrt(%pi)/(gamma(v+3/2))^2*1F2(1;3/2,v+3/2;-z^2/4).

    Raymond> (I'm pretty sure the multiplier is right.  Not sure about the 1F2
    Raymond> form, because it puts the pfq part in a strange way.)

    Raymond> So it does look like our definition of hstruve is exactly as you say.

    Raymond> Now the question is what to do.  Change the our definition to match
    Raymond> DLMF and A&S?  Or just document that our hstruve is different?

    Raymond> I think we should match DLMS and A&S.  Eventually.

The fix to hstf is simple.  This change makes the test work out
correctly.  But now the test

specint(t^(3/2)*hstruve[1](t^(1/2))*%e^(-p*t),t)

is computed incorrectly.  However, I think it's because maxima doesn't
reduce %f[2,2]([1,7/2],[3/2,5/2],-1/4/p) correctly.  This is a bug in
splitpfq, which I have not yet verified to be correct.  In fact, I
think splitpfq is wrong.  Especially because %f([1,7/2],[5/2,3/2],z)
is produces different results from %f([1,7/2],[3/2,5/2],z), which are
supposed to be the same.

I'll make the fix to hstf, and correct the tests.

If anyone has a reference or derivation for splitpfq[1], I'd appreciate
it.  

Ray

Footnotes: 
[1] splitpfq tries to reduce %f[p,q]([a1,a2...],[c1,c2...],z) to a sum
of %f[p-1,q-1] when am = cn+k for some positive integer k.  I can
derive the result when k = 1, but for larger k, I get stuck.