>>>>> "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.