### Related

##### expintegral_e1

? expintegral_e1;

Calculate

##### expintegral_e1

expintegral_e1 (1);

Calculate

##### expintegral_e1-numer

expintegral_e1(1),numer;

Calculate

##### expintegral_e1

expintegral_e1 (-i*0....

Calculate

##### expintegral_e1-numer

expintegral_e1(0.5),n...

Calculate

##### expintegral_e1

? expintegral_e1;

Calculate

##### expintegral_e1

expintegral_e1 (1);

Calculate

##### expintegral_e1-numer

expintegral_e1(1),numer;

Calculate

##### expintegral_e1

expintegral_e1 (-i*0....

Calculate

##### expintegral_e1-numer

expintegral_e1(0.5),n...

Calculate

### expintegral_e1

Run Example
```(%i1)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
```0.007614;
(%o1)                              0.007614
(%i2) h=1.2845051992/8*exp(0.0510449888674/8)*(expintegral_e1(0.0510449888674/8));
(%o2)                        h = 0.72451618979263
(%i3)        f(x):= exp(-x^2/8)/(0.0510449888674+x^2)*x*bessel_j(0, x*r);
2
- x
exp(----)
8
(%o3)           f(x) := -------------------- x bessel_j(0, x r)
2
0.0510449888674 + x
1.2845051992                          0.0510449888674
(%o4) z(r) := ------------ first(quad_qagi(f(x), x, ---------------, inf))
4                                       8
(%i5) z(0);
(%o5)                          0.72438817953262
(%i6) z(0.1);
(%o6)                          0.72128525978964
(%i7) z(0.2);
(%o7)                          0.71216378066744
(%i8) z(0.3);
(%o8)                          0.69756127563698
(%i9) z(0.4);
(%o9)                          0.67829750611763
(%i10) z(0.5);
(%o10)                         0.65537606890704
(%i11) z(0.6);
(%o11)                         0.62987389903861
(%i12) z(0.7);
(%o12)                          0.6028372683398
(%i13) z(0.8);
(%o13)                         0.57519905097187
(%i14) z(0.9);
(%o14)                         0.54772558709599
(%i15) z(1.1);
(%o15)                         0.49539885567193
(%i16) z(1.2);
(%o16)                         0.47117039991325
(%i17) z(1.3);
(%o17)                         0.44841218727665
(%i18) z(1.4);
(%o18)                          0.4271339213045
(%i19) z(1.5);
(%o19)                         0.40728401753358
(%i20) z(1.6);
(%o20)                         0.38877562556127
(%i21) z(1.7);
(%o21)                          0.3715057133891
(%i22) z(1.8);
(%o22)                         0.35536775519309
(%i23) z(1.9);
(%o23)                         0.34025928362266
(%i24) z(1);
(%o24)                         0.52099447277484
(%i25) z(2);
(%o25)                         0.32608574887881
(%i26) z(3);
(%o26)                         0.22105338348782
(%i27) z(4);
(%o27)                         0.15631454210339
(%i28) z(5);
(%o28)                          0.1132577292421
(%i29) z(7);
(%o29)                         0.062071631521718
(%i30) z(10);
(%o30)                         0.026730396546648
(%i31) z(15);
(%o31)                        0.0070582558439069
(%i32) z(20);
(%o32)                        0.0018984006828888
(%i33) ```
Run Example
```0.007614;
(%o1)                              0.007614
(%i2) h=1.78522833333/8*exp(0.008156283/8)*(expintegral_e1(0.008156283/8));
(%o2)                        h = 1.410029279106771
(%i3)        f(x):= exp(-x^2/8)/(0.008156283+x^2)*x*bessel_j(0, x*r);
2
- x
exp(----)
8
(%o3)             f(x) := ---------------- x bessel_j(0, x r)
2
0.008156283 + x
1.78522833333                          0.008156283
(%o4)  z(r) := ------------- first(quad_qagi(f(x), x, -----------, inf))
4                                     8
(%i5) z(0);
(%o5)                          1.41000084180441
(%i6) z(0.1);
(%o6)                          1.405588716456923
(%i7) z(0.2);
(%o7)                          1.392613998169457
(%i8) z(0.3);
(%o8)                          1.371827786347374
(%i9) z(0.4);
(%o9)                          1.344375816239947
(%i10) z(0.5);
(%o10)                         1.311661311951937
(%i11) z(0.6);
(%o11)                         1.275190930001239
(%i12) z(0.7);
(%o12)                         1.236429700303262
(%i13) z(0.8);
(%o13)                         1.196685546049791
(%i14) z(0.9);
(%o14)                         1.157035001953056
(%i15) z(1.1);
(%o15)                         1.081013601214107
(%i16) z(1.2);
(%o16)                         1.045531738795096
(%i17) z(1.3);
(%o17)                         1.011998886732325
(%i18) z(1.4);
(%o18)                         0.98043696202204
(%i19) z(1.5);
(%o19)                          0.9507819521861
(%i20) z(1.6);
(%o20)                         0.92292013263861
(%i21) z(1.7);
(%o21)                         0.89671465417455
(%i22) z(1.8);
(%o22)                         0.87202324350123
(%i23) z(1.9);
(%o23)                         0.84870876378487
(%i24) z(1);
(%o24)                         1.118292001848344
(%i25) z(2);
(%o25)                         0.82664463663169
(%i26) z(3);
(%o26)                         0.65514549585822
(%i27) z(4);
(%o27)                          0.5380745942868
(%i28) z(5);
(%o28)                         0.45118760709172
(%i29) z(7);
(%o29)                         0.32926449252043
(%i30) z(10);
(%o30)                         0.21642789060372
(%i31) z(15);
(%o31)                         0.11554596846957
(%i32) z(20);
(%o32)                         0.064661017334702
(%i33) ```

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