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expintegral_si

expintegral_si (0.1);

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expintegral_si

expintegral_si(1);

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expintegral_si

expintegral_si (1.35);

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expintegral_si

expintegral_si (2) ;

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expintegral_si

expintegral_si(%pi);

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expintegral_si

expintegral_si(0.1);

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expintegral_si

expintegral_si (0.1);

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expintegral_si

expintegral_si (0.1);

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expintegral_si

expintegral_si(0.99);

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expintegral_si

? expintegral_si;

Calculate

expintegral_si

Run Example
(%i1)expintegral_si(0.99);
(%o1)                          0.93765334201444
(%i2) 
Run Example
assume (p >
 0, a >
 0);
(%o1)                           [p > 0, a > 0]
(%i2)  specint (t^(1/2) * exp(-a*t/4) * exp(-p*t), t);
                                  sqrt(%pi)
(%o2)                            ------------
                                        a 3/2
                                 2 (p + -)
                                        4
(%i3)  specint (t^(1/2) * bessel_j(1, 2 * a^(1/2) * t^(1/2))                        * exp(-p*t), t);
                                          - a/p
                                sqrt(a) %e
(%o3)                           ---------------
                                       2
                                      p
(%i4)  assume(s>
0,a>
0,s-a>
0);
(%o4)                      [s > 0, redundant, s > a]
(%i5)  ratsimp(specint(%e^(a*t)*(log(a)+expintegral_e1(a*t))*%e^(-s*t),t));
                                    log(s)
(%o5)                               ------
                                    s - a
(%i6)  logarc:true;
(%o6)                                true
(%i7)  gamma_expand:true;
(%o7)                                true
(%i8)  radcan(specint((cos(t)*expintegral_si(t)                               -sin(t)*expintegral_ci(t))*%e^(-s*t),t));
                                    log(s)
(%o8)                               ------
                                     2
                                    s  + 1
(%i9)  ratsimp(specint((2*t*log(a)+2/a*sin(a*t)                                -2*t*expintegral_ci(a*t))*%e^(-s*t),t));
                                      2    2
                                 log(s  + a )
(%o9)                            ------------
                                       2
                                      s
(%i10)  assume(s>
0);
(%o10)                            [redundant]
(%i11)  specint(1/sqrt(%pi*t)*unit_step(t-k)*%e^(-s*t),t);
                             erfc(sqrt(k) sqrt(s))
(%o11)                       ---------------------
                                    sqrt(s)
(%i12)  gamma_expand:true;
(%o12)                               true
(%i13)  specint(1/sqrt(%pi*t)*unit_step(t-k)*%e^(-s*t),t);
                             erfc(sqrt(k) sqrt(s))
(%o13)                       ---------------------
                                    sqrt(s)
(%i14)  expintrep:expintegral_e1;
(%o14)                          expintegral_e1
(%i15)  ratsimp(specint(1/(t+a)^2*%e^(-s*t),t));
                              a s
                        a s %e    expintegral_e1(a s) - 1
(%o15)                - ---------------------------------
                                        a
(%i16) 
Run Example
expintegral_si(0.999);
(%o1)                           0.9452414488379
(%i2) 

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