← Back to branch summary

~ubuntu-branches/debian/squeeze/maxima/squeeze

« back to all changes in this revision

Viewing changes to tests/rtest14.mac

  • Committer: Bazaar Package Importer
  • Author(s): Camm Maguire
  • Date: 2010-04-30 13:30:33 UTC
  • mto: This revision was merged to the branch mainline in revision 12.
  • Revision ID: james.westby@ubuntu.com-20100430133033-wtewap0zdnmsix1y
Tags: upstream-5.21.1
Import upstream version 5.21.1

Show diffs side-by-side

added added

removed removed

Lines of Context:
tests/rtest14.mac
41
41
true$
42
42
 
43
43
bessel_j(1/2,x);
44
 
sqrt(2/(%pi*x))*sin(x);
 
44
sqrt(2/%pi)*sin(x)/sqrt(x);
45
45
bessel_j(-1/2,x);
46
 
sqrt(2/(%pi*x))*cos(x);
 
46
sqrt(2/%pi)*cos(x)/sqrt(x);
47
47
 
48
48
bessel_j(3/2,x);
49
49
(sqrt(2)*sqrt(x)*(sin(x)/x^2-cos(x)/x))/sqrt(%pi);
57
57
ratsimp(bessel_j(-5/2,x) - (2*(-3/2)/x*bessel_j(-3/2,x)-bessel_j(-1/2,x)));
58
58
0$
59
59
 
60
 
ratsimp(bessel_y(1/2,x) + sqrt(2/(%pi*x))*cos(x));
 
60
ratsimp(bessel_y(1/2,x) + sqrt(2/%pi)*cos(x)/sqrt(x));
61
61
0$
62
62
 
63
 
ratsimp(bessel_y(-1/2,x) - sqrt(2/(%pi*x))*sin(x));
 
63
ratsimp(bessel_y(-1/2,x) - sqrt(2/%pi)*sin(x)/sqrt(x));
64
64
0$
65
65
 
66
66
ratsimp(bessel_y(3/2,x) - (2*(1/2)/x*bessel_y(1/2,x)-bessel_y(-1/2,x)));
93
93
ratsimp(bessel_i(-5/2,x) - (2*(-3/2)/x*bessel_i(-3/2,x)+bessel_i(-1/2,x)));
94
94
0$
95
95
 
96
 
ratsimp(bessel_k(1/2,x) - sqrt(%pi/(2*x))*%e^(-x));
 
96
ratsimp(bessel_k(1/2,x) - sqrt(%pi/2)*%e^(-x)/sqrt(x));
97
97
0$
98
98
 
99
 
ratsimp(bessel_k(-1/2,x)- sqrt(%pi/(2*x))*%e^(-x));
 
99
ratsimp(bessel_k(-1/2,x)- sqrt(%pi/2)*%e^(-x)/sqrt(x));
100
100
0$
101
101
 
102
102
ratsimp(bessel_k(3/2,x) - (2*(1/2)/x*bessel_k(1/2,x)+bessel_k(-1/2,x)));
459
459
 *
460
460
 */
461
461
 
462
 
specint(t*hankel_1(2/3,t^(1/2))*%e^(-p*t),t);
 
462
ratsimp(specint(t*hankel_1(2/3,t^(1/2))*%e^(-p*t),t));
 
463
/* Because of revision 1.110 of hyp.lisp Maxima knows in addition 
 
464
 *    hgfred([7/3],[5/3],-1/(4*x)), 
 
465
 * the result is in terms of the bessel_i function.
 
466
 
463
467
-4*%i*gamma(1/3)*%m[-3/2,1/3](-1/(4*p))*%e^-(1/(8*p))/(3*(-1)^(5/6)*sqrt(3) 
464
468
 *gamma(2/3)*p^(3/2))+4*gamma(1/3)*%m[-3/2,1/3](-1/(4*p))*%e^-(1/(8*p))/(3*( 
465
469
 -1)^(5/6)*gamma(2/3)*p^(3/2))-8*%i*gamma(2/3)*%m[-3/2,-1/3](-1/(4*p))*%e^- 
466
 
 (1/(8*p))/(3*(-1)^(1/6)*sqrt(3)*gamma(1/3)*p^(3/2)) $
 
470
 (1/(8*p))/(3*(-1)^(1/6)*sqrt(3)*gamma(1/3)*p^(3/2)) $ */
 
471
 
 
472
(((-1)^(1/6)*2^(2/3)*sqrt(3)*%i-3*(-1)^(1/6)*2^(2/3))
 
473
        *gamma(1/3)^2*gamma(5/6)*bessel_i(11/6,-1/(8*p))
 
474
        +10*(-1)^(5/6)*sqrt(3)*4^(2/3)*%i*gamma(1/6)*gamma(2/3)^2
 
475
           *bessel_i(7/6,-1/(8*p))
 
476
        +(45*(-1)^(1/6)*2^(2/3)-5*(-1)^(1/6)*2^(2/3)*3^(3/2)*%i)
 
477
         *gamma(1/3)^2*gamma(5/6)*bessel_i(5/6,-1/(8*p))
 
478
        +((9*(-1)^(1/6)*2^(5/3)-(-1)^(1/6)*2^(5/3)*3^(3/2)*%i)
 
479
         *bessel_i(-1/6,-1/(8*p))
 
480
         +(5*(-1)^(1/6)*2^(5/3)*sqrt(3)*%i-15*(-1)^(1/6)*2^(5/3))
 
481
          *bessel_i(-7/6,-1/(8*p)))
 
482
         *gamma(1/3)^2*gamma(5/6)
 
483
        +(((-1)^(5/6)*sqrt(3)*4^(2/3)*%i*bessel_i(-11/6,-1/(8*p))
 
484
         -5*(-1)^(5/6)*3^(3/2)*4^(2/3)*%i*bessel_i(-5/6,-1/(8*p)))
 
485
         *gamma(1/6)
 
486
         -2*(-1)^(5/6)*3^(3/2)*4^(2/3)*%i*gamma(1/6)*bessel_i(1/6,-1/(8*p)))
 
487
         *gamma(2/3)^2)
 
488
        *%e^-(1/(8*p))
 
489
        /(15*2^(13/3)*4^(1/3)*gamma(1/3)*gamma(2/3)*p^(7/2))/-1;
467
490
 
468
491
/*
469
492
 * hankel_2(2,t) = bessel_j(3/4,t)-%i*bessel_y(3/4,t)
704
727
 * (31)
705
728
 * t^(-v/2)*bessel_j(v,2*sqrt(a)*sqrt(t)) ->
706
729
 *    exp(%i*v*%pi)*p^(v-1)/a^(v/2)/gamma(v)*exp(-a/p)*
707
 
 *     %gammagreek(v,a/p*exp(-%i*%pi)
 
730
 *     gamma_greek(v,a/p*exp(-%i*%pi)
708
731
 *
709
 
 * %gammagreek is the incomplete gamma function.
 
732
 * gamma_greek is the incomplete gamma function.
710
733
 */
711
734
specint(t^(-v/2)*bessel_j(v,2*sqrt(a)*sqrt(t))*exp(-p*t),t);
712
 
p^(v-1)*%e^-(a/p)*v*%gammagreek(v,-a/p)/(a^(v/2)*(-1)^v*gamma(v+1))$
 
735
p^(v-1)*%e^-(a/p)*v*gamma_greek(v,-a/p)/(a^(v/2)*(-1)^v*gamma(v+1))$
713
736
 
714
737
/*
715
738
 * (32)
716
739
 * t^(v/2-1)*bessel_j(v,2*sqrt(a)*sqrt(t)) ->
717
 
 *    a^(-v/2)*%gammagreek(v,a/p)
 
740
 *    a^(-v/2)*gamma_greek(v,a/p)
718
741
 */
719
742
specint(t^(v/2-1)*bessel_j(v,2*sqrt(a)*sqrt(t))*exp(-p*t),t);
720
 
v*gamma(v)*%gammagreek(v,a/p)/(a^(v/2)*gamma(v+1))$
 
743
v*gamma(v)*gamma_greek(v,a/p)/(a^(v/2)*gamma(v+1))$
721
744
 
722
745
/*
723
746
 * (34)