sparse SciMax Toolbox spherical_bessel_j

SciMax Toolbox >> specint

specint

Maxima Function

Calling Sequence

specint (exp(- s*t) * expr, t)

Description

Compute the Laplace transform of expr with respect to the variable t. The integrand expr may contain special functions.

If specint cannot compute the integral, the return value may contain various Lisp symbols, including other-defint-to-follow-negtest, other-lt-exponential-to-follow, product-of-y-with-nofract-indices, etc.; this is a bug.

demo(hypgeo) displays several examples of Laplace transforms computed by specint.

Examples:

(%i1) 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
sparse SciMax Toolbox spherical_bessel_j