>>>>> "Wolfgang" == Wolfgang Jenkner writes:
Wolfgang> +(/* This is the Laplace transform of the Struve H_1 function, see
Wolfgang> + http://dlmf.nist.gov/Draft/ST/about_ST.8.13.html */
Wolfgang> + 2/(%pi*p)-2*p*log(p/(sqrt(p^2+1)-1))/(%pi*sqrt(p^2+1)),
Wolfgang> + /* And this should be the same as the specint of the next test below */
Wolfgang> + -diff(%%,p),
Wolfgang> + ev(fullratsimp(%%),logexpand:all));
Wolfgang> +-(sqrt(p^2+1)*(2*p^2*log(sqrt(p^2+1)-1)-2*p^2*log(p))-2*p^2-2)
Wolfgang> + /(%pi*p^6+2*%pi*p^4+%pi*p^2)$
Wolfgang> +
Wolfgang> +(ev(fullratsimp(specint(t*hstruve[1](t)*%e^(-p*t),t)),logexpand:all),
Wolfgang> + ratsimp(%%/%));
Wolfgang> +/* Well, except for a fishy constant factor... */
Wolfgang> +4/(3*sqrt(%pi))$
Thanks for looking this up!
But, if I understand your derivation correctly, the ratio should be 1,
not 4/3/sqrt(%pi).
If so, shouldn't the test have an expected result of 1 and then be
flagged as an error?
I note that maxima is also off by a factor of 2/sqrt(%pi) for the
Laplace transform of H_0(t). And at first glance, the transform of
H_1(t) is completely different from the answer given the DLMF.
Ray