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The Maxima on-line user's manual

Algebra Calculator

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Risch Calculator

Risch

Function: risch (<expr>, <x>) Integrates <expr> with respect to <x> using the transcendental case of the Risch algorithm. (The algebraic case of the Risch algorithm has not been implemented.) This currently handles the cases of nested exponentials and logarithms which the main part of integrate cant do. integrate will automatically apply risch if given these cases.

assume (t>0);
assume (T>0);
erfflag:false;
erfflag;
integrate (j*(2*j+1)*exp(-(t/T)*j*(j+1)), j, 0, inf), risch;

erfflag, if false, prevents risch from introducing the erf function in the answer if there were none in the integrand to begin with.

          (%i1) risch (x^2*erf(x), x);
                                                                  2
                       3                      2                - x
                  %pi x  erf(x) + (sqrt(%pi) x  + sqrt(%pi)) %e
          (%o1)   -------------------------------------------------
                                        3 %pi
          (%i2) diff(%, x), ratsimp;
                                       2
          (%o2)                       x  erf(x)

(%o1)                                true
(%i2) 

Risch Example

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