### Related

##### bessel_j-exp-plot2d-sqrt

series(exp(x),x,0);

plot2d(bessel_j(1,sqr...

Calculate

##### bessel_j-bessel_y-plot2d

plot2d(bessel_j(0,x)*...

Calculate

##### bessel_j-exp-expand-plot2d-realpart-sqrt

Ber(n,x):= realpart(e...

plot2d(Ber(0,x),[x,0,...

plot2d(Ber(0,x)/exp(x...

Calculate

h=3/8*exp(0.0125)*(ex...

f(x):= exp(-x^2/8)/(0...

Calculate

0.007614;

h=1.0717/8*exp(0.0081...

f(x):= exp(-x^...

Calculate

##### bessel_j-bessel_y-hankel_1-hankel_2

bessel_j(2/3,0.5);

bessel_y(2/3,0.5);

hankel_1(2/5,0.5);

Calculate

0.007614;

h=1.071135/8*exp(0.00...

f(x):= exp(-x^...

Calculate

##### bessel_j-diff-factor-sqrt-subst

a : diff(bessel_j(0,s...

b : factor(diff(a,x,2...

b1 : subst(0,bessel_j...

Calculate

##### bessel_j-bessel_y-sqrt

smj:sqrt(1/2)*(-1+%i);

bessel_j(0,smj*4.6)*b...

Calculate

##### bessel_j-integrate-sqrt

integrate(x*bessel_j(...

Calculate

### bessel_j

Run Example
(%i1)a : diff(bessel_j(0,sqrt(t^2-x^2-y^2-z^2)),t)/t ;
2    2    2    2
bessel_j(1, sqrt(- z  - y  - x  + t ))
(%o1)              - --------------------------------------
2    2    2    2
sqrt(- z  - y  - x  + t )
(%i2) b : factor(diff(a,x,2) + diff(a,y,2) + diff(a,z,2) - diff(a,t,2));
2    2    2    2           2    2    2    2
(%o2) (2 bessel_j(2, sqrt(- z  - y  - x  + t )) sqrt(- z  - y  - x  + t )
2    2    2    2           2    2    2    2
- 2 bessel_j(0, sqrt(- z  - y  - x  + t )) sqrt(- z  - y  - x  + t )
2    2    2    2    2
+ bessel_j(3, sqrt(- z  - y  - x  + t )) z
2    2    2    2    2
- 3 bessel_j(1, sqrt(- z  - y  - x  + t )) z
2    2    2    2    2
+ bessel_j(3, sqrt(- z  - y  - x  + t )) y
2    2    2    2    2
- 3 bessel_j(1, sqrt(- z  - y  - x  + t )) y
2    2    2    2    2
+ bessel_j(3, sqrt(- z  - y  - x  + t )) x
2    2    2    2    2
- 3 bessel_j(1, sqrt(- z  - y  - x  + t )) x
2    2    2    2    2
- bessel_j(3, sqrt(- z  - y  - x  + t )) t
2    2    2    2    2
+ 3 bessel_j(1, sqrt(- z  - y  - x  + t )) t
2    2    2    2
+ 4 bessel_j(1, sqrt(- z  - y  - x  + t )))
2    2    2    2    2    2    2    2
/(4 sqrt(- z  - y  - x  + t ) (z  + y  + x  - t ))
(%i3) collectterms(b,bessel_j(1, sqrt(- z^2  - y^2  - x^2  + t^2 ))) ;
2    2    2    2           2    2    2    2
(%o3) (2 bessel_j(2, sqrt(- z  - y  - x  + t )) sqrt(- z  - y  - x  + t )
2    2    2    2           2    2    2    2
- 2 bessel_j(0, sqrt(- z  - y  - x  + t )) sqrt(- z  - y  - x  + t )
2    2    2    2    2
+ bessel_j(3, sqrt(- z  - y  - x  + t )) z
2    2    2    2    2
- 3 bessel_j(1, sqrt(- z  - y  - x  + t )) z
2    2    2    2    2
+ bessel_j(3, sqrt(- z  - y  - x  + t )) y
2    2    2    2    2
- 3 bessel_j(1, sqrt(- z  - y  - x  + t )) y
2    2    2    2    2
+ bessel_j(3, sqrt(- z  - y  - x  + t )) x
2    2    2    2    2
- 3 bessel_j(1, sqrt(- z  - y  - x  + t )) x
2    2    2    2    2
- bessel_j(3, sqrt(- z  - y  - x  + t )) t
2    2    2    2    2
+ 3 bessel_j(1, sqrt(- z  - y  - x  + t )) t
2    2    2    2
+ 4 bessel_j(1, sqrt(- z  - y  - x  + t )))
2    2    2    2    2    2    2    2
/(4 sqrt(- z  - y  - x  + t ) (z  + y  + x  - t ))
(%i4)
Run Example
w=0.007614;
(%o1)                            w = 0.007614
(%i2) h=1/8*exp(w/8)*(expintegral_e1(w/8));
w/8                w
%e    expintegral_e1(-)
8
(%o2)                     h = -----------------------
8
(%i3)        f(x):= exp(-x^2/8)/(w+x^2)*x*bessel_j(0, x*r);
2
- x
exp(----)
8
(%o3)                f(x) := --------- x bessel_j(0, x r)
2
w + x
1                          w
(%o4)             z(r) := - first(quad_qagi(f(x), x, -, inf))
4                          8
(%i5) z(0);
2
x
- --
8
x %e
(%o5)                             ----------
2
4 (x  + w)
(%i6) z(0.1);
2
x
- --
8
bessel_j(0, 0.1 x) x %e
(%o6)                     ---------------------------
2
4 (x  + w)
(%i7) z(0.2);
2
x
- --
8
bessel_j(0, 0.2 x) x %e
(%o7)                     ---------------------------
2
4 (x  + w)
(%i8) z(0.3);
2
x
- --
8
bessel_j(0, 0.3 x) x %e
(%o8)                     ---------------------------
2
4 (x  + w)
(%i9) z(0.4);
2
x
- --
8
bessel_j(0, 0.4 x) x %e
(%o9)                     ---------------------------
2
4 (x  + w)
(%i10) z(0.5);
2
x
- --
8
bessel_j(0, 0.5 x) x %e
(%o10)                    ---------------------------
2
4 (x  + w)
(%i11) z(0.6);
2
x
- --
8
bessel_j(0, 0.6 x) x %e
(%o11)                    ---------------------------
2
4 (x  + w)
(%i12) z(0.7);
2
x
- --
8
bessel_j(0, 0.7 x) x %e
(%o12)                    ---------------------------
2
4 (x  + w)
(%i13) z(0.8);
2
x
- --
8
bessel_j(0, 0.8 x) x %e
(%o13)                    ---------------------------
2
4 (x  + w)
(%i14) z(0.9);
2
x
- --
8
bessel_j(0, 0.9 x) x %e
(%o14)                    ---------------------------
2
4 (x  + w)
(%i15) z(1.1);
2
x
- --
8
bessel_j(0, 1.1 x) x %e
(%o15)                    ---------------------------
2
4 (x  + w)
(%i16) z(1.2);
2
x
- --
8
bessel_j(0, 1.2 x) x %e
(%o16)                    ---------------------------
2
4 (x  + w)
(%i17) z(1.3);
2
x
- --
8
bessel_j(0, 1.3 x) x %e
(%o17)                    ---------------------------
2
4 (x  + w)
(%i18) z(1.4);
2
x
- --
8
bessel_j(0, 1.4 x) x %e
(%o18)                    ---------------------------
2
4 (x  + w)
(%i19) z(1.5);
2
x
- --
8
bessel_j(0, 1.5 x) x %e
(%o19)                    ---------------------------
2
4 (x  + w)
(%i20) z(1.6);
2
x
- --
8
bessel_j(0, 1.6 x) x %e
(%o20)                    ---------------------------
2
4 (x  + w)
(%i21) z(1.7);
2
x
- --
8
bessel_j(0, 1.7 x) x %e
(%o21)                    ---------------------------
2
4 (x  + w)
(%i22) z(1.8);
2
x
- --
8
bessel_j(0, 1.8 x) x %e
(%o22)                    ---------------------------
2
4 (x  + w)
(%i23) z(1.9);
2
x
- --
8
bessel_j(0, 1.9 x) x %e
(%o23)                    ---------------------------
2
4 (x  + w)
(%i24) z(1);
2
x
- --
8
bessel_j(0, x) x %e
(%o24)                      -----------------------
2
4 (x  + w)
(%i25) z(2);
2
x
- --
8
bessel_j(0, 2 x) x %e
(%o25)                     -------------------------
2
4 (x  + w)
(%i26) z(3);
2
x
- --
8
bessel_j(0, 3 x) x %e
(%o26)                     -------------------------
2
4 (x  + w)
(%i27) z(4);
2
x
- --
8
bessel_j(0, 4 x) x %e
(%o27)                     -------------------------
2
4 (x  + w)
(%i28) z(5);
2
x
- --
8
bessel_j(0, 5 x) x %e
(%o28)                     -------------------------
2
4 (x  + w)
(%i29) z(7);
2
x
- --
8
bessel_j(0, 7 x) x %e
(%o29)                     -------------------------
2
4 (x  + w)
(%i30) z(10);
2
x
- --
8
bessel_j(0, 10 x) x %e
(%o30)                    --------------------------
2
4 (x  + w)
(%i31) z(15);
2
x
- --
8
bessel_j(0, 15 x) x %e
(%o31)                    --------------------------
2
4 (x  + w)
(%i32) z(20);
2
x
- --
8
bessel_j(0, 20 x) x %e
(%o32)                    --------------------------
2
4 (x  + w)
(%i33)
Run Example
bessel_j(0,2.5);
(%o1)                         - 0.048383776468198
(%i2)

### Related Help

Help for Bessel_j