? besselexpand;

Calculate

? 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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