id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
16697,implement symbolic lower incomplete gamma function,rws,,"This is actually a defect because we leave a result from Maxima undefined:
{{{
sage: hypergeometric([1],[b],x).simplify_hypergeometric()
(b - 1)*x^(-b + 1)*e^x*gamma_greek(b - 1, x)
sage: gamma_greek
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
in ()
----> 1 gamma_greek
NameError: name 'gamma_greek' is not defined
}}}
https://en.wikipedia.org/wiki/Incomplete_gamma_function#Lower_incomplete_Gamma_function
Mathematica seems to have Gamma[a,z] for upper and Gamma[a,0,z] for lower; Maple seems to have upper Gamma. `gamma_inc` (the upper one in Sage) gets immediately converted to `gamma(a,x)`. The symbolic functions `gamma_inc==incomplete_gamma` are converted and never returned to the user as expression:
{{{
sage: gamma_inc(x,x,hold=True)
gamma(x, x)
sage: incomplete_gamma(x,x,hold=True)
gamma(x, x)
sage: assume(x>0)
sage: integral(t^(s-1)*e^(-t),t,0,x)
-gamma(s, x) + gamma(s)
}}}
This ticket should deprecate ""incomplete_gamma"" and add the symbolic function `gamma_inc_lower`, leaving open the question of the global alias for and the displayed name of `Function_gamma_inc`.
Previous part of description:
-------------------------------------
1. Provide all three ""user input interfaces"" `gamma_inc`, `incomplete_gamma` and `lower_incomplete_gamma`, and convert the Maxima `gamma_greek` to `-gamma(a, x) + gamma(a)`
2. Provide all three ""user input interfaces"" `gamma_inc`, `incomplete_gamma` and `lower_incomplete_gamma`, and convert to `gamma(a,x)` and `gamma(a,0,x)`n on output
3. Provide all three ""user input interfaces"" `gamma_inc`, `incomplete_gamma` and `lower_incomplete_gamma`, and have `incomplete_gamma` and `lower_incomplete_gamma` as result instead of `gamma(...)'
4. Change the user interface completely to `lower_incomplete_gamma` and `upper_incomplete_gamma`
5. Change the user interface completely to `gamma_inc_lower` and `gamma_inc_upper`
6. Change the user interface completely to `gamma(a,x)` and `gamma(a,0,x)`",defect,closed,major,sage-7.2,symbolics,fixed,"gamma, incomplete, special, functions",kcrisman nbruin,,Ralf Stephan,"Buck Evan, Paul Masson",N/A,,157b268d4ac45de049089e633809f89d2c3ab84e,157b268d4ac45de049089e633809f89d2c3ab84e,#20185,