http://code.activestate.com/recipes/tags/laplace_inversion/2010-03-22T05:00:20-07:00ActiveState Code Recipes2010-03-22T05:00:20-07:00Fernando Nieuwveldthttp://code.activestate.com/recipes/users/4172088/http://code.activestate.com/recipes/577133-a-new-method-for-computing-the-hypergeometric-func/

<p style="color: grey"> Python recipe 577133 by <a href="/recipes/users/4172088/">Fernando Nieuwveldt</a> (<a href="/recipes/tags/function/">function</a>, <a href="/recipes/tags/hypergeometric/">hypergeometric</a>, <a href="/recipes/tags/laplace_inversion/">laplace_inversion</a>). Revision 3. </p> <p>I present a method of computing the 1F1(a,b,x) function using a contour integral. The method is based on a numerical inversion, basically the Laplace inversion. Integral is 1F1(a,b,x) = Gamma(b)/2\pi i \int_\rho exp(zx)z^(-b)(1+x/z)^(-a)dz, \rho is taken as a Talbot contour. The Talbot method is applied with the use of the midpoint rule for numerical integration. Here the user must give the number of function evaluations and this may vary from problem to problem. It is very easy to implement with only a few lines of code and it is very accurate even for large arguments.</p>

2009-11-24T01:20:56-08:00Dieter Kadelkahttp://code.activestate.com/recipes/users/4172107/http://code.activestate.com/recipes/576964-pricing-asian-options-using-mpmath-with-automatic-/

<p style="color: grey"> Python recipe 576964 by <a href="/recipes/users/4172107/">Dieter Kadelka</a> (<a href="/recipes/tags/computational_finance/">computational_finance</a>, <a href="/recipes/tags/laplace_inversion/">laplace_inversion</a>, <a href="/recipes/tags/mpmath/">mpmath</a>). </p> <p>In <a href="http://code.activestate.com/recipes/576954/">Recipe 576954</a> presented a numerical method for pricing Asian options using mpmath and some code from <a href="http://code.activestate.com/recipes/576938/">Recipe 576938</a>: Numerical Inversion of the Laplace Transform with mpmath. The code in <a href="http://code.activestate.com/recipes/576954/">Recipe 576954</a> seems to have problems with the precision required for accurate computation of the integrals. To solve this problem, I changed the code in <a href="http://code.activestate.com/recipes/576938/">Recipe 576938</a> and the code in <a href="http://code.activestate.com/recipes/576954/">Recipe 576954</a>, which now uses mp_laplace.py.</p> <p>The new mp_laplace.py and asian.py are in the code section.</p>