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besselexpand

? besselexpand;

Calculate

besselexpand

? besselexpand;

Calculate

besselexpand

Run Example
(%i1)radexpand:all;
(%o1)                                 all
(%i2) besselexpand:true;
(%o2)                                true
(%i3) assume (q>
0);
(%o3)                               [q > 0]
(%i4) assume (hbarc>
0);
(%o4)                             [hbarc > 0]
(%i5) assume(ce>
0);
(%o5)                              [ce > 0]
(%i6) k:q/hbarc;
                                       q
(%o6)                                -----
                                     hbarc
(%i7) v(r):= r/(r**4+ce);
                                           r
(%o7)                           v(r) := -------
                                         4
                                        r  + ce
(%i8) f(r):=r**(3/2)*v(r)*bessel_j(1/2,k*r);
                               3/2               1
(%o8)                 f(r) := r    v(r) bessel_j(-, k r)
                                                 2
(%i9) r0:integrate(f(r),r,0,inf);
                                        inf  2      q r
                                       /    r  sin(-----)
                                       [           hbarc
                   sqrt(2) sqrt(hbarc) I    ------------- dr
                                       ]        4
                                       /       r  + ce
                                        0
(%o9)              -----------------------------------------
                               sqrt(%pi) sqrt(q)
(%i10) res:r0/(2*%pi)**(3/2)/hbarc**(5/2)/q**(1/2);
                              inf  2      q r
                             /    r  sin(-----)
                             [           hbarc
                             I    ------------- dr
                             ]        4
                             /       r  + ce
                              0
(%o10)                       ---------------------
                                     2      2
                                2 %pi  hbarc  q
(%i11)                                                                                                                                                                                                                                                                                        rex:factor(res);
                              inf  2      q r
                             /    r  sin(-----)
                             [           hbarc
                             I    ------------- dr
                             ]        4
                             /       r  + ce
                              0
(%o11)                       ---------------------
                                     2      2
                                2 %pi  hbarc  q
(%i12)                                                                                                                                                                           print(" V(r)=",v(r));
          r
 V(r)= ------- 
        4
       r  + ce
                                       r
(%o12)                              -------
                                     4
                                    r  + ce
(%i13)                                                                         print("         ");
          
(%o13)                                      
(%i14) print(" V(q)=",rex);
        inf  2      q r
       /    r  sin(-----)
       [           hbarc
       I    ------------- dr
       ]        4
       /       r  + ce
        0
 V(q)= --------------------- 
               2      2
          2 %pi  hbarc  q
                              inf  2      q r
                             /    r  sin(-----)
                             [           hbarc
                             I    ------------- dr
                             ]        4
                             /       r  + ce
                              0
(%o14)                       ---------------------
                                     2      2
                                2 %pi  hbarc  q
(%i15) quit();
Run Example
besselexpand: false;
(%o1)                                false
(%i2)  bessel_i (1/2, sqrt(3));
                                      1
(%o2)                        bessel_i(-, sqrt(3))
                                      2
(%i3)  besselexpand: true;
(%o3)                                true
(%i4)  bessel_i (1/2, sqrt(3));
                             sqrt(2) sinh(sqrt(3))
(%o4)                        ---------------------
                                 1/4
                                3    sqrt(%pi)
(%i5) 
Run Example
besselexpand: false;
(%o1)                                false
(%i2)  bessel_j (3/2, z);
                                         3
(%o2)                           bessel_j(-, z)
                                         2
(%i3)  besselexpand: true;
(%o3)                                true
(%i4)  bessel_j (3/2, z);
                                        sin(z)   cos(z)
                       sqrt(2) sqrt(z) (------ - ------)
                                           2       z
                                          z
(%o4)                  ---------------------------------
                                   sqrt(%pi)
(%i5) 

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