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bessel_j-bessel_y-taylor

taylor(bessel_j(m,c*x...

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

h=1/8*exp(0.0088809/8...

f(x):= exp(-x^2...

z(r):=1/4*(first(q...

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

h=1.79804/8*exp(0.013...

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

z(r):=1.79804/4*(f...

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

h=1/8*exp(0.05611094/...

f(x):= exp(-x^2...

z(r):=1/4*(first(q...

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

0.007614;

h=0.724826945/8*exp(0...

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

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

h=1/8*exp(0.1066/8)*(...

f(x):= exp(-x^2...

z(r):=1/4*(first(q...

Calculate

bessel_j

bessel_j(0,2.5);

Calculate

bessel_j

a:bessel_j(nu,x^2);

b:bessel_j(nu-1,x);

Calculate

bessel_j-create_list-plot2d
plot2d(create_list(bessel_j(n,x),n,1,3), [x,0,10]);

plot2d(create_list(be...

Calculate

bessel_j-create_list-plot2d
plot2d(create_list(bessel_j(n,x),n,1,4), [x,0,10]);

plot2d(create_list(be...

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
(%i4)    z(r):=1/4*(first(quad_qagi(f(x),x,w/8,inf)));
                          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) 

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