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Expintegral_si

Function: expintegral_si (<z>) The Exponential Integral Si(z) (A&S 5.2.1)

assume (p > 0, a > 0);
 specint (t^(1/2) * exp(-a*t/4) * exp(-p*t), t);
 specint (t^(1/2) * bessel_j(1, 2 * a^(1/2) * t^(1/2))                        * exp(-p*t), t);
 assume(s>0,a>0,s-a>0);
 ratsimp(specint(%e^(a*t)*(log(a)+expintegral_e1(a*t))*%e^(-s*t),t));
 logarc:true;
 gamma_expand:true;
 radcan(specint((cos(t)*expintegral_si(t)                               -sin(t)*expintegral_ci(t))*%e^(-s*t),t));
 ratsimp(specint((2*t*log(a)+2/a*sin(a*t)                                -2*t*expintegral_ci(a*t))*%e^(-s*t),t));
 assume(s>0);
 specint(1/sqrt(%pi*t)*unit_step(t-k)*%e^(-s*t),t);
 gamma_expand:true;
 specint(1/sqrt(%pi*t)*unit_step(t-k)*%e^(-s*t),t);
 expintrep:expintegral_e1;
 ratsimp(specint(1/(t+a)^2*%e^(-s*t),t));

(%o1)                                true
(%i2) 

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