## maxima-commits

 [Maxima-commits] CVS: maxima/tests rtest14.mac,1.19,1.20 From: Raymond Toy - 2005-02-27 21:25:03 ```Update of /cvsroot/maxima/maxima/tests In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv31328/tests Modified Files: rtest14.mac Log Message: o Give the correct result for specint(t^(3/2)*hstruve[1](t^(1/2))*%e^(-p*t),t). o Document the derivation. Index: rtest14.mac =================================================================== RCS file: /cvsroot/maxima/maxima/tests/rtest14.mac,v retrieving revision 1.19 retrieving revision 1.20 diff -u -d -r1.19 -r1.20 --- rtest14.mac 27 Feb 2005 02:53:21 -0000 1.19 +++ rtest14.mac 27 Feb 2005 21:24:54 -0000 1.20 @@ -183,16 +183,26 @@ * From the f19p220, the Laplace transform of this, with s = 7/2, * c=-1/4, k = 1, is * - * gamma(7/2)/p^(7/2)*%f[2,2]([1,7/2],[3/2,5/2],-1/4/p) + * 2/(3*%pi)*gamma(7/2)/p^(7/2)*%f[2,2]([1,7/2],[3/2,5/2],-1/4/p) * + * From the derivation of SPLITPFQ, we can simplify this + * hypergeometric function. * + * %f[2,2]([1,7/2],[3/2,5/2],z) = * + * 1 + * sum z^k/poch(5/2,k)*binomial(1,k) *diff(%f[2,2]([1,5/2],[3/2,5/2],z,k) + * k=0 * + * But %f[2,2]([1,5/2],[3/2,5/2],z) = %f[1,1]([1],[3/2],z) + * and Maxima knows how to compute this. */ -radcan(specint(t^(3/2)*hstruve[1](t^(1/2))*%e^(-p*t),t)); -%e^-(1/(4*p))*((140*p^(3/2)+10*sqrt(p))*%e^(1/(4*p))+140*sqrt(%pi)*%i*erf(%i/ - (2*sqrt(p)))*p^2+20*sqrt(%pi)*%i*erf(%i/(2*sqrt(p)))*p+5*sqrt(%pi)*%i*erf - (%i/(2*sqrt(p))))/(8*%pi*p^4) \$ +ratsimp(specint(t^(3/2)*hstruve[1](t^(1/2))*%e^(-p*t),t)); +-%e^-(1/(4*p))*(sqrt(%pi)*sqrt(p) + *(8*%i*erf(%i/(2*sqrt(p)))*p + -%i*erf(%i/(2*sqrt(p)))) + -2*p*%e^(1/(4*p))) + /(8*sqrt(%pi)*p^(9/2)) \$ specint(t*%ibes[0](a*t/2)*%ibes[1](a*t/2)*%e^(-p*t),t); %ibes[0](a*t/2)*%ibes[1](a*t/2)/p^2 \$ ```