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- /* This is a sample of answers from the under construction program,
- which deals with "Bateman's Manuscript Project". */
- DYNAMALLOC:TRUE;
- ASSUME(P > 0);
- SHOWTIME:TRUE$
-
- /* Laplace transforms */
-
- /* Some elementary functions. */
-
- t^(1/2)*%e^(-a*t/4)*%e^(-p*t);
- specint(%,t);
- t^(3/4)*%e^(-t^2/2/b)*%e^(-p*t);
- specint(%,t);
- t^(-1/2)*%e^(-2*a^(1/2)*t^(1/2))*%e^(-p*t);
- specint(%,t);
- t^(1/2)*%e^(-p*t-a/t);
- specint(%,t);
- sin(a*t)*cosh(b*t^2)*%e^(-p*t);
- radcan(specint(%,t));
-
- /* Some "confluents". Notice that "%M[k,m](z)" is a Whittaker function. */
-
- %e^(a*t)*t^2*erf(t^(1/2))*%e^(-p*t);
- specint(%,t);
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- t^(3/2)*%m[1/2,1](t)*%e^(-p*t);
- specint(%,t);
-
-
-
- /* Some Bessel functs (bf's). */
-
- /* %J[v](z), 1st kind of bf's. */
- /* %Y[v](z), 2nd kind of bf's.*/
- /* %H[v,1](z), 1st kind of the 3rd kind of bf's (1st Hankel). */
- /* %H[v,2](z), 2nd kind of the 3rd kind of bf's (2nd Hankel).*/
-
-
-
- t^(1/2)*%j[1](2*a^(1/2)*t^(1/2))*%e^(-p*t);
- specint(%,t);
- t^2*%j[1](a*t)*%e^(-p*t);
- specint(%,t);
-
- t^(3/2)*%y[1](a*t)*%e^(-t);
- specint(%,t);
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- t^(3/2)*%h[1/2,1](t)*%e^(-p*t);
- specint(%,t);
- t^(1/2)*%h[3/4,2](t)*%e^(-p*t);
- specint(%,t);
- t*%h[2/3,1](t^(1/2))*%e^(-p*t);
- specint(%,t);
-
- /* %Ibes[v](z), %K[v](z), Modified bf's. */
-
-
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- t^(1/2)*%ibes[1](t)*%e^(-p*t);
- specint(%,t);
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- %j[1](t)^2*%e^(-p*t+r);
- specint(%,t);
- t^(1/2)*%j[1/2](t^(1/2))^2*%e^(-p*t);
- specint(%,t);
- t^(5/2)*%y[1/2](t^(1/2))^2*%e^(-p*t);
- specint(%,t);
-
- /*Some combinations of products of Bessel functions*/
- t^(3/4)*%j[1/2](t)*%j[1/4](t)*%e^(-p*t);
- specint(%,t);
-
- t*%ibes[0](a*t/2)*%ibes[1](a*t/2)*%e^(-p*t);
- specint(%,t);
-
-
-
- /* Related to bf's functions. */
-
- /* Struve functions. */
-
-
-
- t^(3/2)*hstruve[1](t^(1/2))*%e^(-p*t);
- radcan(specint(%,t));
-
-
- t*hstruve[1](t)*%e^(-p*t);
- specint(%,t);
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