Opened 4 years ago

Last modified 10 months ago

#17737 new enhancement

wrap Maxima's factorial/gamma conversions/expansions

Reported by: rws Owned by:
Priority: major Milestone: sage-wishlist
Component: symbolics Keywords:
Cc: kcrisman, ktkohl, tmonteil Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by rws)

To be most clear to the user (and staying in sync with current ticket discussions) I rather propose four functions:

  • gamma_to_factorial - use simplify_full(?)
  • factorial_to_gamma - use makegamma with maxima.eval("gamma_expand:true")
  • expand_gamma - e.g., gamma(n+1) --> n*gamma(n), use makegamma with maxima.eval("gamma_expand:false"), also gamma_expand
  • simplify_gamma - e.g., n*gamma(n) --> gamma(n+1), use makegamma with maxima.eval("gamma_expand:true"). Could be an alias to 2) or left out.

This ticket will *not include one of these in another simplify* function.

Change History (6)

comment:1 Changed 4 years ago by rws

  • Description modified (diff)

comment:2 Changed 4 years ago by rws

  • Description modified (diff)

comment:3 Changed 4 years ago by rws

  • Milestone changed from sage-6.5 to sage-wishlist

comment:4 Changed 4 years ago by kcrisman

  • Cc kcrisman added

comment:5 Changed 4 years ago by ktkohl

  • Cc ktkohl added

comment:6 Changed 10 months ago by tmonteil

  • Cc tmonteil added

Such a feature would be awesome, in particular in a combinatorial context, it could be nice if Sage were able to transform gamma(n+1/2) into factorial(2n)/(4^n*factorial(n))*sqrt(pi), see e.g. 

sage: var('k,n')
(k, n)
sage: assume(n,'integer')
sage: symbolic_product((2*k)^2-1,k,1,n)
2^(2*n + 1)*gamma(n + 3/2)*gamma(n + 1/2)/pi
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