>>>>> "Wolfgang" == Wolfgang Jenkner writes:
Wolfgang> Raymond Toy writes:
>> But, if I understand your derivation correctly, the ratio should be 1,
>> not 4/3/sqrt(%pi).
Wolfgang> Here is a better answer (I hope ;-)
>> From comparing specint(hstruve[n](t)*%e^(-p*t),t) with the Laplace
Wolfgang> transform of the power series representation
Wolfgang> http://dlmf.nist.gov/Draft/ST/about_ST.3.1.html
Wolfgang> of their Struve H[n] functions one finds (e.g., by applying several
Wolfgang> times the duplication formula for the gamma function) that they could
Wolfgang> be defined as
Wolfgang> H[n](t):=hstruve[n](t)*gamma(n+3/2);
This makes sense now. Assuming I did the math right, ST.3.1 can be
expressed as
H[v](t) = 2*2^(-v-1)*z^(v+1)/sqrt(%pi)/gamma(v+3/2)*1F2(1;3/2,v+3/2;-z^2/4).
If I look at hstf in hypgeo.lisp, it seems that it's returning
2*2^(-v-1)*z^(v+1)/sqrt(%pi)/(gamma(v+3/2))^2*1F2(1;3/2,v+3/2;-z^2/4).
(I'm pretty sure the multiplier is right. Not sure about the 1F2
form, because it puts the pfq part in a strange way.)
So it does look like our definition of hstruve is exactly as you say.
Now the question is what to do. Change the our definition to match
DLMF and A&S? Or just document that our hstruve is different?
I think we should match DLMS and A&S. Eventually.
Ray