## File: hypgeo.dmo

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maxima 5.6-17
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116` ``````/* 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); 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); 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. */ t^(1/2)*%ibes[1](t)*%e^(-p*t); specint(%,t); %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); ``````